Nonlinear Evolution Equations, Quasi-Solitons and their Experimental Manifestation

  • M. Remoissenet
Part of the NATO ASI Series book series (ASIC, volume 310)


We review the typical experimental facts which characterize quasisolitons in one-dimensional real systems, in connection with their modeling by nonlinear partial differential equations.We consider these nonlinear waves or excitations in two different domains of the real world : the macroworld and the microworld. In the macroworld we examine typical one-dimensional devices : the electrical networks, the Josephson transmission lines and the optical fibers, where the localized waves or pulses can be simply and coherently created, easily observed and manipulated on a macroscopic scale. In the microworld, we consider the magnetic chains and polymers, where the indirect experimental signatures of the localized nonlinear excitations are more subtle than for the nonlinear macrowaves. We finally discuss some open problems in the complex and important field of biological chains such as DNA.


Solitary Wave Transmission Line Solitary Wave Solution Toda Lattice Easy Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Section 1:Chapter

  1. Benjamin, T.B. and Feir, J.F. (1967). The désintégration of wavetrains on deep water, J Fluid Mech, 27, 417–430.ADSzbMATHCrossRefGoogle Scholar
  2. Benson, F. A. and Last, D. J. (1965) Nonlinear transmission line harmonic generator. Proc IEEE, 112, 635–643.Google Scholar
  3. Berkhoer, A. L and Zakharov, V. E (1976). Self excitation of waves with different polarizations in nonlinear media, Soviet Phys JETP, 31, 486–489.ADSGoogle Scholar
  4. Chu, P. L. and Whitebread, T. (1978) Applications of solitons to communication system. Electron Lett, 14, 531–532.ADSCrossRefGoogle Scholar
  5. Dodd, R. K. Eilbeck, J. C. Gibbon, J. D. and Morris, H. C. (1984) Solitons and nonlinear wave equations, Academic Press, New York.Google Scholar
  6. Freeman, R. H. and Karbowiack, A. E. (1977) An investigation of nonlinear transmission lines and shock waves. J Phys D: Appl Phys, 10, 633–643.ADSCrossRefGoogle Scholar
  7. Fukushima, K. (1983) Modulated wavetrain in a nonlinear transmission line. J Phys Soc Japan, 52, 376–379.ADSCrossRefGoogle Scholar
  8. Fukushima, K. Wadati, M. and Narahara, Y. (1980) Envelope soliton in a new nonlinear transmission line. J Phys Soc Japan, 49, 1593–1597.ADSCrossRefGoogle Scholar
  9. Fukushima, K. Wadati, M. Kotera, T. Sawada, K. and Narahara, Y. (1980) Experimental and theoretical study of recurrence phenomena in nonlinear transmission line. J Phys Soc Japan, 48, 1029–1034.ADSCrossRefGoogle Scholar
  10. Gasch, A. Wedding, B. and Jäger, D. (1984) Multistability and soliton modes in nonlinear microwave resonators. Appl Phys Lett, 44, 1105–07.ADSCrossRefGoogle Scholar
  11. Hirota, R. and K. Susuki, K. (1973) Theoretical and experimental studies of lattice solitons in nonlinear lumped networks. Proc IEEE, 61, 1483–367.CrossRefGoogle Scholar
  12. Hirota, R. and Susuki, K. (1970) Studies of lattice soliton by using electrical networks. J Phys Soc Japan, 28, 1366–1491.ADSCrossRefGoogle Scholar
  13. Inoue, Y. (1976). Nonlinear coupling of polarized plasma waves, J Plasma Phys, 16, 439–459.ADSCrossRefGoogle Scholar
  14. Inoue, Y. (1977). Nonlinear interaction of dispersive waves with equal group velocity, J Phys Soc Japan, 16, 243–249.ADSGoogle Scholar
  15. Jäger, D. (1978) Soliton propagation along periodic transmission lines. Appl Phys, 16, 35–38.ADSCrossRefGoogle Scholar
  16. Jäger, D.(1982) Experiments on KdV solitons. J Phys Soc Japan, 51, 1686–1693.ADSCrossRefGoogle Scholar
  17. Kako, F. (1979) Propagation of solitons in a dissipative transmission line. J Phys Soc Japan, 47, 1686–1692.MathSciNetADSCrossRefGoogle Scholar
  18. Karpman, V. I. and Maslov. (1978) E. M. Perturbation theory for solitons, Sov Phys JETP, 46, 281–291.MathSciNetADSGoogle Scholar
  19. Karpman, V. I. and Krushkal, E. M. (1969). Modulated waves in nonlinear dispersive media. Sov Phys JETP, 28, 277–281.ADSGoogle Scholar
  20. Kawata, T. Sakai, J. and Inoue, H. (1977) Nonlinear dispersive waves and parametric interaction in the transmission line, 60, 339–346.Google Scholar
  21. Kofane, T. Michaux, B. and Remoissenet, M. (1988) Theoretical and experimental studies of diatomic lattice solitons using an electrical transmission line. J Phys C: Solid State Phys, 21, 1395–1412.ADSCrossRefGoogle Scholar
  22. Kolosick, J. A. Landt, D. L. Hsuan, H. C. and Lonngreen, K. E. (1974) Properties of solitary waves as observed on a nonlinear dispersive transmission line. Proc IEEE, 62, 578–581.CrossRefGoogle Scholar
  23. Kuusela, T and Hietarinta, J. (1989) Elastic scattering of solitary waves in the strongly dissipative Toda lattice, Phys Rev Lett, 62, 700–703.ADSCrossRefGoogle Scholar
  24. Kuusela, T. Hietarinta, J. Kolko, K. and Larbro, R. (1987) Soliton experiments in a nonlinear electrical transmission line. Eur J Phys, 8, 27–33.CrossRefGoogle Scholar
  25. Landt, D. L. (1972) An experimental simulation of waves in plasmas. Am J Phys, 40, 1493–1497.ADSCrossRefGoogle Scholar
  26. Longreen K. E. (1978) ‘ Observation of solitons on nonlinear dispersive transmission lines ’ in Lonngreen, K. and Scott, A. C. (Eds) Solitons in action. Academic Press, New York, pp 127–152.Google Scholar
  27. Mankankov, V. G. (1978) Dynamics of classical solitons. Physics Reports, 35, 2–128.ADSGoogle Scholar
  28. Muroya, K. Saitoh, N. and Watanabe, S (1982) Experiment on lattice soliton by nonlinear LC circuit, observation of a dark soliton, J Phys Soc Japan, 51, 1024–1029.ADSCrossRefGoogle Scholar
  29. Nagashima, H. and Amagishi, H. (1979) Experiment on solitons in the dissipative Toda lattice using nonlinear transmission lines. J Phys Soc Japan, 47, 2021–2027.ADSCrossRefGoogle Scholar
  30. Nagashima, H. and Amagishi, Y. (1978) Experiment on the Toda lattice using nonlinear transmission lines. J Phys Soc Japan, 45, 680–688.ADSCrossRefGoogle Scholar
  31. Nejoh, Y. (1985) Envelope soliton of the electron plasma wave in a nonlinear transmission line. Phys Script, 31, 415–418.ADSCrossRefGoogle Scholar
  32. Newell, A. C. (1985). Solitons in mathematics and physics, Soc for Ind and Appl Maths, Philadelphia.Google Scholar
  33. Noguchi, A. (1974) Solitons in a nonlinear transmission line. Elec and Commun Japan. 57A, 9–13.ADSGoogle Scholar
  34. Ostrovskii, L. A and Papko, V. V. (1972) Solitary electromagenetic waves in nonlinear lines. Radiophysics, 15, 438–446.MathSciNetCrossRefGoogle Scholar
  35. Paulus, P. Wedding, B. Gasch, A. and Jäger, D. (1984) Bistability and solitons observed in a nonlinear ring resonator. Phys Lett, 102A, 89–92.ADSGoogle Scholar
  36. Peterson, G. E. (1984) Electrical transmission lines as models forsoliton propagation in materials: elementary aspect of video solitons. AT§TBell Lab Tech J, 63, 901–919.Google Scholar
  37. Sakai, J. and Kawata, T. (1976) Nonlinear wave modulation in the transmission line. J Phys Soc Japan, 41, 1819–1820.ADSCrossRefGoogle Scholar
  38. Scott, A. C. (1970) Active and nonlinear wave propagation in electronics. Wiley Interscience, New York.Google Scholar
  39. Spatschek, K. H. (1978). Coupled localized electron-plasma waves and oscillatory ion-acoustic perturbations, Phys Fluids, 21, 1032–1035.ADSzbMATHCrossRefGoogle Scholar
  40. Suzuki, K. Hirota and Yoshikawa, K. (1973) The properties of phase modulated soliton trains. Jap J Appl Phys, 12, 361–365.ADSCrossRefGoogle Scholar
  41. Suzuki, K. Hirota, R. and Yoshikawa, K. (1973) Amplitude modulated soliton trains and coding-decoding applications. Int J Electron, 34, 777.CrossRefGoogle Scholar
  42. Takagi, K. (1983) The power spectrum of a white noise passed through a nonlinear transmisión line. Jpn J Appl Phys. 22, 1466.ADSCrossRefGoogle Scholar
  43. Tan, M. Su, C.Y. and Anklam, W.J. (1988) 7. electrical pulse compression on an inhomogeneous nonlinear transmission line. Electron Lett, 24, 213–215.CrossRefGoogle Scholar
  44. Taniuti, T. and Yajima, N. (1969) Perturbation method for a nonlinear wave modulation. J Math Phys, 10, 1369–1372MathSciNetADSCrossRefGoogle Scholar
  45. Toda, M (1967) Vibrations of a chain with nonlinear interaction. J Phys Soc Japan, 22, 431–436.ADSCrossRefGoogle Scholar
  46. Toda, M. (1970) Waves in nonlinear lattice. Prog Theor Phys Japan Suppl. 45, 174–201.ADSCrossRefGoogle Scholar
  47. Watanabe, S. (1982) Solitons in nonlinear transmission line. J Phys Soc Japan, 51, 1030–1036.ADSCrossRefGoogle Scholar
  48. Watanabe, S. Miyakawa, M. and Muroya, K. (1980) Experiment on recurrence in nonlinear LC circuit. J Phys Soc Japan, 48, 825–831.ADSGoogle Scholar
  49. Watanabe, S. Miyakawa, M. and Toda, M. (1978) Asymptotic behavior of collisionless shock in nonlinear LC circuit. J Phys Soc Japan, 45, 2030.ADSCrossRefGoogle Scholar
  50. Yagi, T and Noguchi, A. (1977) Gyromagnetic nonlinear element and its application as a pulse-shaping transmission line. Electron Letters, 13, 683–685.CrossRefGoogle Scholar
  51. Yagi, T. and Noguchi, A. (1976) Experimental studies on modulational instability by using nonlinear transmission lines. Elec and Commun in Japan, 59A, 1–6.Google Scholar
  52. Yazaki, T and Fukushima, K. (1985) Experimental studies of potential problems in quantum mechanics. Am J Phys, 53, 1186–1191.ADSCrossRefGoogle Scholar
  53. Yoshinaga, T. and Kakutani, T. (1980) Solitary and shock waves on a coupled transmission line. J Phys Soc Japan, 49, 2072–2074.ADSCrossRefGoogle Scholar
  54. Yoshinaga, T. and Kakutani, T. (1984) Second order KDV soliton on a nonlinear transmission line, J Phys Soc Japan, 53, 85–92.ADSCrossRefGoogle Scholar
  55. Yoshinaga, T.Sugimoto, N and Kakutani, T. (1981) Nonlinear wave interactions on a discrete transmission line; J. Phys Soc Japan, 50, 2122–2128.MathSciNetADSCrossRefGoogle Scholar

Section 2:Chapter

  1. Barone, A. and Paterno, G. (1982) Physics and application of the Josephson effect. Wiley, New York.CrossRefGoogle Scholar
  2. Chen, J. T. Finnegan, T. F. and Langenberg, D. N. (1971) Physica 55, 413.ADSCrossRefGoogle Scholar
  3. Costabile, G and Parmentier, R. D. (1975) Analytic solution for fluxon propagation in Josephson junctions with bias and loss, in low Temperature Physics - LT 14, vol. 14, M. Krusius and M. Vuorio Eds, North Holland, Amsterdam, pp. 112–115.Google Scholar
  4. Costabile, G. Parmentier, R. D. Savo, B. Mac Laughlin, D. W and Scott, A. C. (1978) Exact solutions in a long (but finite) Josephson junction. Appl. Phys. Lett. 32, 587–589.ADSCrossRefGoogle Scholar
  5. Davidson, A. Ducholm, B. and Pedersen, N. F. (1986) Experiments on soliton motion in annular Josephson Junctions. J. Appl. Phys., 60, 1447–1454.ADSCrossRefGoogle Scholar
  6. Feyman, R.P. (1960) Lectures on Physics, Vol. 3 section 21.9. Addison Wesley, New York.Google Scholar
  7. Fujmaki, A. Nakajima, K. and Sawada, Y. (1987) Spatiotemporal observation of the Soliton-Antisoliton collision in Josephson Transmission line. Phys. Rev. Lett., 59, 2895–2198.ADSCrossRefGoogle Scholar
  8. Fulton, T. A. Magerlein, J. H. and Dynes, R. C. (1976) A Josephson logic design employing current switching junctions. AS 76, 56.Google Scholar
  9. Harris, R. E. (1974) Cosine and other terms in the Josephson tunneling current. Phys. Rev. B. 10, 84–94.ADSCrossRefGoogle Scholar
  10. Josephson, B. D. (1962) Possible new effects in superconductor tunneling. Phys. Lett. 1, 251–253.ADSzbMATHCrossRefGoogle Scholar
  11. Josephson, B. D. (1965) Supercurrents through barriers. Adv. Phys. 14, 419–451. see also (1964) Coupled superconductors. Rev Mod Phys, 36, 216–220.ADSCrossRefGoogle Scholar
  12. Levring, O. A. Perdersen, N. F and Samulsen, M. R. (1982) Fluxon motion in long overlap and inline Josephson Junctions Appl. Phys. Lett. 40, 846–847.ADSCrossRefGoogle Scholar
  13. Likharev. K. K. (1986) Dynamics of Josephson junctions and circuits. Gordon and Breach, New York.Google Scholar
  14. Lomdahl, P. S. (1985) Solitons in Josephson junctions: an overview, J Stat Phys, 39, 5/6, 551–561.ADSCrossRefGoogle Scholar
  15. Lomsdahl, P. S. Soerensen, O. H. and Christiansen, P. L. (1982). Soliton excitations in Josephson tunnel junctions. Phys Rev. B, 25, 5737–5748.ADSCrossRefGoogle Scholar
  16. Matsuda, A and Kawakami, T. (1983) Fluxon propagation on a Josephson Transmission line. Phys. Rev. Lett., 51, 695–697.ADSCrossRefGoogle Scholar
  17. Matsuda, A. (1986) Observation of fluxon-antifluxon collision in a Josephson transmission line. Phys. Rev. B, 34, 3127–3135.ADSCrossRefGoogle Scholar
  18. Matsuda, A. and Uheara, S. (1982) Observation of fluxon propagation on Josephson transmission line. Appl. Phys. Lett., 41, 770–772.ADSCrossRefGoogle Scholar
  19. Me Laughlin, D. W. and Scott, A. C. (1978) Perturbation analysis of fluxon motion. Phys. Rev. A, 18, 1652–1680.ADSCrossRefGoogle Scholar
  20. Nitta, J. Matsuda, A and Kawakami, T. (1984) Propagation properties of fluxons in a well damped Josephson transmission line. 55, 2758–2762.Google Scholar
  21. Pagano, S. (1987) Nonlinear dynamics in long Josephson junctions, PhD Thesis, Technical Univ of Denmark, Lingby, Denmark.Google Scholar
  22. Parmentier (1978).Fluxons in long Josephson Junctions, in Solitons in action, Eds K. Lonngreen and A. C. Scott, Academic Press, New York, pp 173–199.Google Scholar
  23. Pedersen, N. F and Welner, D. (1984) Comparison between experiments and perturbation theory for solitons in Josephson junctions. Phys. Rev. B, 29, 2551.ADSCrossRefGoogle Scholar
  24. Pedersen, N. F. (1989) Nonlinear properties of Josephson Junctions. Proceedings of the ASI Summerschool on superconducting electronics, Ciccio, Italy Plenum.Google Scholar
  25. Scott, A. C. Chu, F. Y. F. and Reible, S. A. (1976) Magnetic flux propagation on a Josephson transmission line. J. Appl. Phys. 47, 3272–3286.ADSCrossRefGoogle Scholar
  26. Pedersen, N. F. Samuelsen, M. R. and Welner, D. (1984) Soliton annhilation in the perturbed Sine Gordon system, Phys. Rev. B, 30, 4057–4059.ADSCrossRefGoogle Scholar
  27. Scott, A. C. (1964) Distributed device application of the superconducting tunnel junction. Solid State Elee 7, 137–146.ADSCrossRefGoogle Scholar
  28. Scott, A. C. (1969) A nonlinear Klein-Gordon equation, Am J Phys, 37, 52–61.ADSCrossRefGoogle Scholar
  29. Swihart, J. C. (1961). Field solution for a thin film superconducting strip line. J. Appl. Phys. 32 461–469.ADSCrossRefGoogle Scholar

Section 3:Chapter

  1. Agrawal, G. P. Baldeck, P. L. and Alfano, R. R. (1989) Modulational instability induced by cross-phase modulation in optical fibers. Phys Rev A, 39, 3406–3413.ADSCrossRefGoogle Scholar
  2. Beaud, P. Hodel, W. Zysset, B. and Weber, H.P (1987) Ultrashort pulse propagation, pulse breakup and fundamental soliton formation in a single mode optical fiber. IEEE J. Quant. Electron, QE.23, 1938–1946.ADSCrossRefGoogle Scholar
  3. Blow, J. and Doran, N. J.(1987) Nonlinear effects in optical fibres and fibre devices. IEEE Proc, 134, 138–144.Google Scholar
  4. Blow, K. J. and Doran, N. J. (1985) The asymptotic dispersion of soliton pulses in lossy fibres. Opt Commun, 52, 367–370.ADSCrossRefGoogle Scholar
  5. Bourkoff, E. Zhao, W. R. I. Joseph, R. I and Christotoulides, D. N. (1987) Evolution of femtosecond pulses in single mode fibers having higher order nonlinearity and dispersion. Opt. Lett., 12, 272–274.ADSCrossRefGoogle Scholar
  6. Cotter, D. (1982) Observation of stimulated Brillouin scattering in low loss silica fiber at 1.3μ m. Electron Lett., 18, 495–496.CrossRefGoogle Scholar
  7. Cotter, D. (1982) Transient stimulated Brillouin scattering in long single mode fibers. Electron Lett., 18, 504–506.CrossRefGoogle Scholar
  8. Cristodoulides, D. N. and Joseph, R. I. (1985) Femtosecond solitary waves in optical fibers, beyond the slowly varying envelope approximation. Appl Phys Lett, 47, 76–78.ADSCrossRefGoogle Scholar
  9. Doran, N. J and Blow, K. J. (1983). Solitons in optical communications. IEEE J Qant Electron. QE-19, 1883–1888.ADSCrossRefGoogle Scholar
  10. Firth, W. Peyghambarian, N. and Tallet, A. (1988) Eds, Proceedings of the Int Conf on optical bistability IV, Aussois, France, Part IV, J Phys, Coll C 2, Suppl 6, 49, C-277–342.Google Scholar
  11. Gloge, D. (1979) The optical fiber as a transmission medium. Rep Prog Phys, 42, 1777–1824.ADSCrossRefGoogle Scholar
  12. Hasegawa, A. and Brinkman, W. F.(1980) Tunable coherent IR and FIR sources utilizing modulational instability. IEEE J. Quant Electron, QE-16, 694–697.ADSGoogle Scholar
  13. Hasegawa, A.(1983) Amplification and reshaping of optical soliton in a glass fiber. 4 Use of stimulated Raman process. Opt. Lett. 8, 650.ADSCrossRefGoogle Scholar
  14. Hasegawa, A. (1984) Generation of a train of soliton pulses by induced modulational instability in optical fibers. Opt. Lett, 9, 288290.CrossRefGoogle Scholar
  15. Hasegawa, A. and Kodama, Y. (1981) Signal transmission by optical solitons in monomode fiber. Proc. IEEE, 69, 1145–1150.ADSCrossRefGoogle Scholar
  16. Hasegawa, A. and Tappert, F. (1973a) Transmission of stationnary nonlinear optical pulses in dispersive dielectric fibers-1. Anomalous dispersion. Appl. Phys. Lett, 23, 142–144.ADSCrossRefGoogle Scholar
  17. Hasegawa, A. and Tappert, F. (1973b) Transmission of stationary linear optical pulses in dispersive dielectric fibers-2. Normal dispersion Appl. Phys. Lett. 23, 146–149.Google Scholar
  18. Jain, M. and Tzoar, N. (1978) Propagation of nonlinear optical pulses in inhomogeneous media. J. Appl Phys, 49, 4649–4654. ibid Nonlinear pulse propagation in optical fibers. Opt Lett, 3, 202–204.ADSCrossRefGoogle Scholar
  19. Jain, M. and Tzoar, N.(1987) Nonlinear pulse propagation in a monomode dielectric guide. IEEE J Qant Elec, QE-23, 510.Google Scholar
  20. Kaminov, I. P. (1981) Polarization in optical fibers. IEEE Qant Elec, QE-17, 15–22.ADSCrossRefGoogle Scholar
  21. Karpman, V. I. (1975), Nonlinear wave in dispersive media. Pergamon Press, NewYork.Google Scholar
  22. Kodama, Y. (1985) Optical solitons in a monomode fiber. J Phys Stat, 39, 5/6, 597–614.MathSciNetCrossRefGoogle Scholar
  23. Kodama, Y. and Ablowitz, M. J. (1980) Perturbations of solitons and solitary waves. Stud. Appl. Math, 64, 225–245.MathSciNetGoogle Scholar
  24. Kodama, Y. and Hasegawa, A. (1987) Nonlinear pulse propagation in a monomode dielectric guide. IEEE J Quant Elec. QE-23, 510–524.ADSCrossRefGoogle Scholar
  25. Krokel, D. Halas, N. J. Gianlani, G and Grischowsky, D. (1988) dark pulse propagation in optical fibers. Phys Rev Lett, 60, 29–32.ADSCrossRefGoogle Scholar
  26. Menyuk, C.R. (1987a) Nonlinear pulse propagation in birefringent optical fibers. IEEE J. Quant. Electron, QE-23, 174–176.Google Scholar
  27. Menyuk, C. R. (1987b) Stability of solitons in birefringent optical fibers. I. equal propagation amplitudes. Opt Lett, 12, 614–616ADSCrossRefGoogle Scholar
  28. Menyuk, C. R. (1988) Stability of solitons in birefringent optical fibers. II Arbitrary amplitudes. Opt Lett., 5, 392–402.Google Scholar
  29. Mitscke, F. M. and Mollenauer, L. F. (1986) Discovery of the soliton self frequency shift. Opt. Lett, 11, 659–661.ADSCrossRefGoogle Scholar
  30. Mollenauer and K. Smith. (1988) Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated bh Raman gain. Opt. Lett., 13, 675–677.ADSCrossRefGoogle Scholar
  31. Mollenauer, L. F. and Stolen, R. H. (1984) The soliton laser. Opt lett. 9, 13.ADSCrossRefGoogle Scholar
  32. Mollenauer, L. F. and Stolen, R. H. (1982) Solitons in optical fibers. Fiberoptic Technology, April, 193–198.Google Scholar
  33. Mollenauer, L. F. Stolen, R. H. and Islam, M. N. (1985) Experimental demonstration of soliton propagation in long films: loss compensated by Raman gain. Opt. Lett. 10, 229–231.ADSCrossRefGoogle Scholar
  34. Mollenauer, L. F. Stolen, R. H. and Gordon, J. P. (1980) Experimental observation of picosecond pulse narrowing and solitons in optical fibers, Phys. Rev. Lett, 45, 1095–1098.ADSCrossRefGoogle Scholar
  35. Mollenauer, L. F. Stolen, R. H. and Gordon, J. P. and Tomlinson, W. J.(1983) Extreme picosecond pulse narrowing by means of soliton effect in single mode optical fibers. Optics Letter, 8, 289–291.ADSCrossRefGoogle Scholar
  36. Salin, F. Grangier. P. Roger, G and Brun, A. (1986) Observation of high order solitons produced by a picosecond ring laser. Phys. Rev. Lett. 56, 1132–1135.ADSCrossRefGoogle Scholar
  37. Satsuma, J. and Yajima, S. (1974) Initial value problems of one dimensional self modulation of nonlinear waves in dispersive media. Prog. Theor. Phys. Suppl., 55, 284–306.MathSciNetADSCrossRefGoogle Scholar
  38. Stegeman, G. I. and Stolen, R. H. (1988) Eds. Nonlinear guided wave phenomena in Optical Physics »Special issue, J Opt Soc Am B, 5.Google Scholar
  39. Stolen, R. H. Mollenauer, L. F and Tomlinson, W. J. (1983) Observation of pulse restoration at the soliton period in optical fibers Opt. Lett. 8, 186–188.ADSCrossRefGoogle Scholar
  40. Tai, K. Hasegawa, A. and Tomita, A. (1986) Observation of modulation instability in optical fibers. Phys. Rev. Lett., 56, 135–138.ADSCrossRefGoogle Scholar
  41. Taniuti, T. (1974) Reductive perturbative method and far fields of wave equations. Phys. Theor. Phys. (Japan), Suppl. 55, 1.ADSGoogle Scholar
  42. Tratruk, M. V. and Sipe, J. E. (1988) Bound solitary waves in a birefringent optical fiber. Phys. Rev. A 38, 2011–2017.ADSCrossRefGoogle Scholar
  43. Wabnitz, C. R. (1988) Modulational polarization instability of light in a nonlinear birefringent dispersive medium. Phys. Rev. A, 38, 2018–2021.ADSCrossRefGoogle Scholar
  44. Wai, P. K. Menyuk, C. R. Chen, H and Lee Y. C. (1986) Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers. Opt. Lett, 11, 464–466.ADSCrossRefGoogle Scholar
  45. Wai, P. K. Menyuk, C. R. Chen, H and Lee Y. C. (1987) Solitons at the zero dispersion wavelength of a single mode fiber. Opt Lett, 12, 628–630.ADSCrossRefGoogle Scholar
  46. Zakharov, V. E. and Shabat, A. B. (1972) Exact theory of two dimensional self focusing and one dimensional self modulation of waves in nonlinear media. Sov. Phys. JETP, 34, 62–69.MathSciNetADSGoogle Scholar
  47. Zhakarov, V. E. and Shabat, A. B. (1973) Interaction between solitons in a stable medium. Sov. Phys. JETP, 37, 823–828.ADSGoogle Scholar
  48. Zhao, Wand Bourkoff, E. (1988) Femtosecond pulse propagation in optical fibers: higher order effects. IEEE J. Quant Electron., 24, 365–372.ADSCrossRefGoogle Scholar

Section 4:Chapter

  1. Balakrishnan, R. and Bishop, A. R. (1985) Nonlinear Excitations on a quantum ferromagnetic chain. Phys Rev Lett, 55, 537–540.MathSciNetADSCrossRefGoogle Scholar
  2. Balucani, U. Lovesey, S. W., Rasetti, M. G. and Tognetti, V. Eds. (1984) Magnetic excitations and fluctuations. Springer Proceedings in Physics. Springer Verlag_Berlin.Google Scholar
  3. Balucani, U. Lovesey, S. W., Rasetti, M. G. and Tognetti, V. Eds. (1987) Magnetic excitations and fluctuations II. Springer Proceedings in Physics 23. Springer Verlag_Jerlin.Google Scholar
  4. Bhakta, J. C. (1987) A pair of coupled equations for high frequency Langmuir and dispersive ion- acoustic waves with collisional damping. Plasma Phys and Controlled Fusion. 29, 245–255.ADSCrossRefGoogle Scholar
  5. Birgeneau, R. J. and Shirane, G (1978). Magnetism in one dimension. Physics Today, 32, Dec.Google Scholar
  6. Borsa, F. Pini, M. G. Rettori, A. and Tognetti, V. (1983) Magnetic specific heat contributions from linear vis à vis nonlinear excitations in the one dimensional antiferromagnet TMMC. Phys Rev B, 28, 5173–5183.ADSCrossRefGoogle Scholar
  7. Boucher, J. P. (1980)Solid State Commun, 33, 1025.ADSCrossRefGoogle Scholar
  8. Boucher, J. P. (1989). Nonlinear excitations in antiferromagnetic chains. To be published in Proceedings of Nuclear in magnetism. Munich, August 1988.Google Scholar
  9. Boucher, J. P. and Renard, J. P. (1980) Nuclear spin lattice relaxation by solitons in the antiferromagnetic chains (CH3)4 NMnCl3. Phys Rev Lett, 45, 486–489.ADSCrossRefGoogle Scholar
  10. Boucher, J. P. Pynn, R. Remoissenet, M. Regnault, L. P Endoh, Y. and Renard, J. P. (1989). Newdouble-magnons modes in planar antiferromagnets: a newstudy by polarised-neutron, inelastic scattering of TMMC in a transverse field, to be published.Google Scholar
  11. Boucher, J. P. Regnault, L. P. and Benner, H. (1987) Soliton dynamics: experiments on magnetic chains, p 24 In Nonlinearity in condensed matter. Eds A. R. Bishop, D. K. Campbell, P. Kumar and S. E. Trullinger. Springer, Berlin.Google Scholar
  12. Boucher, J. P. Regnault, L. P. Rossat Mignot, J. and Henri, Y. (1984) in “Magnetic Excitations and Fluctuations”. Eds F. Lovesey, U. Balucani, F. Borsa and V. Tognetti. Springer, Berlin.Google Scholar
  13. Boucher, J. P. Regnault, L. P. Rossat Mignot, J. Renard, J. P. Bouillot, J and Stirling, W. G. (1981) J Appl Phys, 52, 1956–1960.ADSCrossRefGoogle Scholar
  14. Cieplak, M. and Turski, L. A. (1980) Solitons in quantum Heisenberg chain. J Phys C, 13, 5741–5747.ADSCrossRefGoogle Scholar
  15. Corones, J. (1977) Solitons as nonlinear magnons. Phys Rev B, 16, 1763–1764.ADSCrossRefGoogle Scholar
  16. Cowley, R. A., Buyers, W. L. Martel, P. and Stevenson, R. W. (1969) Two magnon scattering of neutrons. Phys Rev Lett, 23, 86–89.ADSCrossRefGoogle Scholar
  17. De Gronckel, H. A. De Jonge, W. J. Kopinga, K. and Lemmens, L. F. (1988) Thermal conductivity of some soliton-bearing magnetic systems. Phys Rev B, 37, 9915–9918.ADSCrossRefGoogle Scholar
  18. De Groot, H. J. M. De Jonge, L. J. Elmassalami, M. Schmitt. H. H. and Thiel, R. C. (1986) Mössbauer relaxation studies of nonlinear dynamics excitations in low-dimensional magnets. Hyperfine Interactions, 27, 93.ADSCrossRefGoogle Scholar
  19. Fogedby, H. C. (1980) Solitons and magnons in the classical Heisenberg chain. J Phys A, 13, 1467–1499.MathSciNetADSCrossRefGoogle Scholar
  20. Gouvea, M. E and Pires, A, S. (1986) Nonlinear excitations in the classical one-dimensional antiferromagnet. Phys Rev B, 34, 306–317.ADSCrossRefGoogle Scholar
  21. Izyumov, Y. A. (1989) Solitons in quasi one dimensional magnetic materials and their study by neutron scattering. Sov Phys Usp, to be published.Google Scholar
  22. Kopinga, K. and De Jonge, W. J. (1987) Linear and nonlinear excitations in the S=1/2 ferromagnetic chain system [C6H11NH3] CuBr3 (CHAB), p 167, in Magnetic excitations and fluctuations II. U. Balucani, S. W. Lovesey, M. G. Rasetti and V. Tognetti Eds. Springer Proceedings in Physics 23. Springer Verlag, Berlin.Google Scholar
  23. Kakurai, K. Steiner, M. Pynn, R and Dorner, B. (1986) Study of the linear and nonlinear excitations in CsNiF3, by means of polarized neutron scattering. J Mag and Mag Mat, 54–57, 835–836.CrossRefGoogle Scholar
  24. Kumar, P. (1982) Soliton instability in one-dimensional magnet. Phys. Rev. B 25, 483–486.ADSCrossRefGoogle Scholar
  25. Laksmanan, M. (1977) Heisenberg continuum system as an exactly solvable dynamical system. Phys Lett, 53, 53–54.Google Scholar
  26. Lindgärd, P. A. (1984), p 163, in Condensed Matter research using neutrons. Eds S. W. Lovesey and R. Scherm. Nato ASI series. Plenum, NewYork.Google Scholar
  27. Magyari, E and Thomas, H. (1982) Kink instability in planar ferromagnets. Phys. Rev. B, 25, 531–533.ADSCrossRefGoogle Scholar
  28. Makankov, V. G. and Fedyanin, V. K. (1984) Nonlinear effects in quasi-one-dimensional models of condensed matter theory. Phys Rep, 104, 1–86.MathSciNetADSCrossRefGoogle Scholar
  29. Maki, K. (1980) Quantum statistics of solitons, p 63 in Physics in one dimension. Eds Bernasconi, J. and Schneider, T. Springer, Berlin.Google Scholar
  30. Maki, K.(1981) Quantum effects in quasi-one dimensional magnetic systems. Phys Rev B, 24, 3991–332.ADSCrossRefGoogle Scholar
  31. Mikeska, H. J. (1981) Solitons in one dimensional ferromagnets. J. Appl. Phys., 52, 1950–1955.ADSCrossRefGoogle Scholar
  32. Mikeska, H. J. (1982) Soliton energy in an easy plane quantum spin chain. Phys Rev B, 26, 5213–5222.MathSciNetADSCrossRefGoogle Scholar
  33. Mikeska, H. J. (1978) Solitons in one-dimensional magnet whith an easy plane. J. Phys. C 11, L29–L32.CrossRefGoogle Scholar
  34. Mikeska, H. J. (1980) Nonlinear dynamics of classical one dimensional ferromagnets. J. Phys. C, 13, 2913–2923.ADSCrossRefGoogle Scholar
  35. Ramirez, A. P. and wolf, W, P. (1982) Specific of CsNiF3: evidence for spin solitons. Phys Rev Lett, 49, 227–229.ADSCrossRefGoogle Scholar
  36. Regnault, L. P. Boucher, J. P. Rossat Mignot, J. Renard, J. P. Bouillot, J. and Stirling, W. G. (1982) A neutron investigation of the soliton regime in the one-dimensional planar antiferromagnet (CD3) NMnCb(CD3). J Phys C, 15, 1261–1282.ADSCrossRefGoogle Scholar
  37. Remoissenet, M. (1986). Lowamplitude breather and envelope solitons in quasi-one-dimensional physical models. Phys Rev B, 33, 2386–2392.ADSCrossRefGoogle Scholar
  38. Remoissenet, M. (1989) Real lattices modelled by the nonlinear Schrödinger equation and its generalization, in Proceedings of workshop “Integrable systems and applications”, Oléron, France June 1988. To be published in Lecture Notes in Mathematics (or Physics). Springer, Berlin.Google Scholar
  39. Sahadevan, R. Tamizhmani, K. M. and Lakshmanan, M. (1986) Painlevé analysis and integrability of coumled nonlinear Schrodinger equations. J Phys A: Math Gen, 19, 1783–1791.MathSciNetADSzbMATHCrossRefGoogle Scholar
  40. Steiner, M. Kakurai, K. and Kjems, J. K. (1983) Experimental studies of the spin dynamics in the 1D ferromagnet with planar anisotropy, CsNiF3, in an external magnetic field J. Magn Mat Mater, 15–18, 1057.Google Scholar
  41. Steiner, M. and Kjems, J. K. (1978) Solitons in CSNÍF3: their experimental evidence and their thermodynamics, p 191 in solitons and condensed matter physics. Eds Bishop, A. R. and Schneider J. Springer, Berlin.Google Scholar
  42. Tjon, J. and Wright, J. (1977) Solitons in the continuous Heisenberg chain. Phys Rev B, 15, 3470–3476.ADSCrossRefGoogle Scholar
  43. Villain, J. (1975) Physica. Propagative spin relaxation in the Ising-like antiferromagnetic linear chain. 79B, 1–12.Google Scholar
  44. Wysin, G and Kumar, P. (1987) Thermomagnetic transport coefficients: solitons in an easy plane magnetic chain. Phys Rev B, 13, 7063–7070.ADSCrossRefGoogle Scholar
  45. Wysin, G. Bishop, A. R and Kumar, P. (1982) Solitons dynamics on a ferromagnetic chain. J. Phys. C, 15, L337–L344.ADSCrossRefGoogle Scholar
  46. Wysin, G. Bishop, A. R and Kumar, P. (1984) Soliton dynamics on an easy plane ferromagnetic chain J. Phys. C, 17, 5975–5992.ADSCrossRefGoogle Scholar
  47. Wysin, G. Bishop, A. R and Oitmaa, A. R. (1986) Single kink dynamics in an easy plane classical antiferromagnetic chain. J Phys C, 19, 221–235.ADSCrossRefGoogle Scholar
  48. Zhakarov, V. E. and Schulman, E.I. (1982) To the integrability of the system of two coupled nonlinear Schrödinger squations. Physica 4D, 270–274.ADSGoogle Scholar

Section 5:Chapter

  1. Balanovski, E. (1987). The physics of DNA: onset of sloliton-like excitations, chain relative disorder, and basis for a stastical mechanics of the macromolecule. Int J Theor Phys, 26, 49–61.zbMATHCrossRefGoogle Scholar
  2. Balanowski, E. and Beaconsfield, P. (1985). Solitonlike excitations in biological systems. Phys. Rev. A, 32, 3059–3064.ADSCrossRefGoogle Scholar
  3. Banerjee, A. and Sobell, H. M. (1983). Presence of nonlinear excitations in DNA structure and their relationnship to DNA permelting and to drug intercalation. J. Biomol struct. Dyn, 1, 253–262.Google Scholar
  4. Barthés, M. (1989) Optical anomalies in acetanalide Davydov solitons, localised modes or Fermi resonance ? To be published in J Mol Liq, special issue.Google Scholar
  5. Baverstock, K. F. and Cundall, R. B. (1988). Solitons and energy transfer in DNA. Nature, 322, March 24, 312–313.ADSCrossRefGoogle Scholar
  6. Careri, G. Buontempo, U. Galluzi, F. Gratton, E. and Scott, A.C. (1984). Spectroscopic evidence of Davydov like solitons in Acetanilide. Phys. Rev. B, 30, 4689–4703.ADSCrossRefGoogle Scholar
  7. Cottingham, J. P. and Scheiwtzer, J. W. (1989) Calculation of the lifetime of a Davydov soliton at finite temperature. Phys Rev Lett, 62, 1792–1795.ADSCrossRefGoogle Scholar
  8. Davydov, A. S. (1985). Solitons in Molecular Systems, Reidel, Dordrecht.zbMATHGoogle Scholar
  9. Del Giudice, Doglia, S. and Milani, M. (1982) A collective dynamics in metabolically active cells. Phys Script, 26, 232–238.ADSCrossRefGoogle Scholar
  10. Dickerson, R. E. (1983). The DNA helix and howit is read. Sci Amer, December, 87–104.Google Scholar
  11. Englander, S.W. Kallenbach, N. R. Heeger, A. J. Krumhansl, J. A. and Litwin, S. (1980) Nature of the open state in long polynucleotide double helixes: possibility of solitons excitations, Proc Nat Acad Sei USA, 777, 7222–7226.ADSCrossRefGoogle Scholar
  12. Frank-Kamenitskii, M. D. (1985) Fluctational motility of DNA, p 47 in Structure and motions: menbranes, nucleic acids and proteins. Ed E. Clementi, G; Corongiu, M. H. Sarma R. H. Sarma. Adenine Press, NewYork.Google Scholar
  13. Freifelder, D. (1987). Molecular biology. Jones and Bartlett, Publishers, Boston.Google Scholar
  14. Friedland, P. and Kedes, L. H. (1985) Discovering the secrets of DNA. Commun of ACM, 28, 1164–1186.CrossRefGoogle Scholar
  15. Fröhlich, H (1969), Quantum mechanical concepts in biology, p 13 in Theoretical Physics and Biology, Eds Marois, North Holland, Amsterdam.Google Scholar
  16. Fröhlich, H. (1968). Long range coherence and energy storage in biological systems. Int J Quant Chern, II, 641–649.ADSCrossRefGoogle Scholar
  17. Heeger, A. J, Kivelson, S, Schrieffer J. R. and Su, W. P. (1988) Solitons in conducting polymers. Rev Mod Phys, 60, 781–850.ADSCrossRefGoogle Scholar
  18. Homma, S and Takeno, S. (1984). A coupled base-rotator model for structure and dynamics of DNA, Prog Theor Phys, 72, 679–693.MathSciNetADSzbMATHCrossRefGoogle Scholar
  19. Hyman, J. M. Mc Laughlin, D.W. and Scott, A. C. (1981). On Davydov’s a- Helix solitons. Physica D, 3D, 23.ADSCrossRefGoogle Scholar
  20. Kim, Y. and Prohofsky, E. W. (1987). Vibrational modes of a DNA polymer at low temperature. Phys. Rev. B, 36, 3449–3451.ADSCrossRefGoogle Scholar
  21. Krumhansl, J. A. and Alexander, D. M. (1983). Nonlinear dynamics and conformai excitations in biomolecular materials. In structure and Dynamics: Nuclear acids and proteins. Ed. E. Clemente and R. H Sarma. Adenine Press, NewYork.Google Scholar
  22. Krumhansl, J. A. Wysin, G.M. Alexander, D. M. Garcia, A. Lomdahl, P.S. Scott P. Layne (1985). Further theoretical studies of (nonlinear) conformational motions in double-helix DNA, 407–415, in Structure and motions: menbranes, nucleic acids and proteins. Ed E. Clementi, G; Corongiu, M. H. Sarma R. H. Sarma. Adenine Press, NewYork.Google Scholar
  23. Lewitt, M. (1982). Computer Simulation of DNA Double-helix dynamics Cold Spring Harbor Symp Quant Biol, 46A, 251–262.Google Scholar
  24. Lilley, D. M. (1988). DNA opens up, supercoiling and heavy breathing, TIG, 4, 111–121.CrossRefGoogle Scholar
  25. Lomdahl, P.S. Layne, S.P. and Bigio, I. J. Solitons in biology (1985). Los Alamos Sciences, Spring Issue, 4–21.Google Scholar
  26. Lomdahl, P.S. Mac Neil, L. Scott, A. C. Stoneham, M. E. and Webb, S.J. (1982). An assignment to internal soliton vibrations of Laser Raman from living cells. Phys. Lett. 92 A, 207–210.ADSGoogle Scholar
  27. Mei, W. N. Kohli, M. Prohofsky, E. W. and Van Zandt, L.L. (1981) Acoustic modes and nonbounded interactions of the double helix. Biopolymers, 20, 833–852.CrossRefGoogle Scholar
  28. Muto, V. Halding, J. Christiansen P. L. and Scott, A. C. (1988) Solitons in DNA. J Biomol Struct and Dyn, 5, 873–874.Google Scholar
  29. Muto, V. Scott, A. C. and Christiansen, P. L. (1989). Thermally generated solitons in DNA. PreprintGoogle Scholar
  30. Peyrard, M. and Bishop, A. R. (1989) Statistical mechanics of a nonlinear model for DNA denaturation. Preprint.Google Scholar
  31. Prohofsky, E. W. (1988) Solitons hiding in DNA and their possible significance in RNA transcription. Phys Rev B, 38, 1538–1554.ADSGoogle Scholar
  32. Saenger, W. (1984). Principles of nucleic acid structure, Springer, NewYork.Google Scholar
  33. Scott, A. C. (1982a). Dynamics of Davydov solitons. Phys. Rev. B, 26, 578–595.ADSGoogle Scholar
  34. Scott, A. C. (1982b) The vibrational structure of Davydov soliton. Phys. Script. 35, 651–672.ADSCrossRefGoogle Scholar
  35. Scott, A. C. (1985a). Solitons in biological molecules. Comments Moll. Cell. Biophys., 3, 15–37.Google Scholar
  36. Scott, A. C. (1985b). Soliton oscillations in DNA, Phys Rev A, 31, 3518–3519.MathSciNetADSCrossRefGoogle Scholar
  37. Scott, A.C.(1985c). Anharmonic analysis of resonant microwave absorption in DNA, Phys Script, 36, 617–638.ADSCrossRefGoogle Scholar
  38. Sobell, H. M. (1984). Kink - antikink bound states in DNA structure, p 172 in Structure of biological molecules and assemblies. Vol. II. F. Jurnak and A. Mc Pherson eds, Wiley, NewYork.Google Scholar
  39. Szent-Giörgyi, A. (1941) The study of energy levels in biochemistry. Nature, 148, 157–159.ADSCrossRefGoogle Scholar
  40. Takeno, S. and Homma, S. (1987). Kinks and breathers associated with collective sugar puckering in DNA. Prog. Theor. Phys. 77, 548–562.MathSciNetADSCrossRefGoogle Scholar
  41. Tuszynski, J. A. Paul, R. Chatterjee, R. and Sreenivasan, S.R. (1984). Relationship between Fröhlich an Davydov models of biological order, Phys Rev A, 30, 2666–2675.ADSCrossRefGoogle Scholar
  42. Wang, X. Brown, D. W. and Linenberg, K. (1989) Quantum Monte Carlo simulation of the Davydov model. Phys Rev Lett, 1796–1799.Google Scholar
  43. Xiao, J. Lin, J. and Zhang, G. (1987). The influence of longitudinal vibration on soliton excitation in DNA double helices, J Phys A, 20, 2425–2432.MathSciNetADSCrossRefGoogle Scholar
  44. Yomosa, S. (1983). Soliton excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. A, 27, 2120–2125.MathSciNetADSCrossRefGoogle Scholar
  45. Yomosa, S. (1984). Solitary excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. A, 30, 474–480.ADSCrossRefGoogle Scholar
  46. Zhakarov, V.E. (1972). Collapse of Langmuir waves. Sov. Phys. JETP, 72, 908–919.ADSGoogle Scholar
  47. Zhang, G. (1987) Soliton excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. II, 35, 886–891.ADSCrossRefGoogle Scholar
  48. Ziman, J. Electrons and phonons: the theory of transport phenomena in Solids. Clarendon, Oxford, 1980Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • M. Remoissenet
    • 1
  1. 1.Laboratoire O. R. CUniversité de BourgogneDijonFrance

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