Abstract
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.
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References
Section 1:Chapter
Benjamin, T.B. and Feir, J.F. (1967). The désintégration of wavetrains on deep water, J Fluid Mech, 27, 417–430.
Benson, F. A. and Last, D. J. (1965) Nonlinear transmission line harmonic generator. Proc IEEE, 112, 635–643.
Berkhoer, A. L and Zakharov, V. E (1976). Self excitation of waves with different polarizations in nonlinear media, Soviet Phys JETP, 31, 486–489.
Chu, P. L. and Whitebread, T. (1978) Applications of solitons to communication system. Electron Lett, 14, 531–532.
Dodd, R. K. Eilbeck, J. C. Gibbon, J. D. and Morris, H. C. (1984) Solitons and nonlinear wave equations, Academic Press, New York.
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.
Fukushima, K. (1983) Modulated wavetrain in a nonlinear transmission line. J Phys Soc Japan, 52, 376–379.
Fukushima, K. Wadati, M. and Narahara, Y. (1980) Envelope soliton in a new nonlinear transmission line. J Phys Soc Japan, 49, 1593–1597.
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.
Gasch, A. Wedding, B. and Jäger, D. (1984) Multistability and soliton modes in nonlinear microwave resonators. Appl Phys Lett, 44, 1105–07.
Hirota, R. and K. Susuki, K. (1973) Theoretical and experimental studies of lattice solitons in nonlinear lumped networks. Proc IEEE, 61, 1483–367.
Hirota, R. and Susuki, K. (1970) Studies of lattice soliton by using electrical networks. J Phys Soc Japan, 28, 1366–1491.
Inoue, Y. (1976). Nonlinear coupling of polarized plasma waves, J Plasma Phys, 16, 439–459.
Inoue, Y. (1977). Nonlinear interaction of dispersive waves with equal group velocity, J Phys Soc Japan, 16, 243–249.
Jäger, D. (1978) Soliton propagation along periodic transmission lines. Appl Phys, 16, 35–38.
Jäger, D.(1982) Experiments on KdV solitons. J Phys Soc Japan, 51, 1686–1693.
Kako, F. (1979) Propagation of solitons in a dissipative transmission line. J Phys Soc Japan, 47, 1686–1692.
Karpman, V. I. and Maslov. (1978) E. M. Perturbation theory for solitons, Sov Phys JETP, 46, 281–291.
Karpman, V. I. and Krushkal, E. M. (1969). Modulated waves in nonlinear dispersive media. Sov Phys JETP, 28, 277–281.
Kawata, T. Sakai, J. and Inoue, H. (1977) Nonlinear dispersive waves and parametric interaction in the transmission line, 60, 339–346.
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.
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.
Kuusela, T and Hietarinta, J. (1989) Elastic scattering of solitary waves in the strongly dissipative Toda lattice, Phys Rev Lett, 62, 700–703.
Kuusela, T. Hietarinta, J. Kolko, K. and Larbro, R. (1987) Soliton experiments in a nonlinear electrical transmission line. Eur J Phys, 8, 27–33.
Landt, D. L. (1972) An experimental simulation of waves in plasmas. Am J Phys, 40, 1493–1497.
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.
Mankankov, V. G. (1978) Dynamics of classical solitons. Physics Reports, 35, 2–128.
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.
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.
Nagashima, H. and Amagishi, Y. (1978) Experiment on the Toda lattice using nonlinear transmission lines. J Phys Soc Japan, 45, 680–688.
Nejoh, Y. (1985) Envelope soliton of the electron plasma wave in a nonlinear transmission line. Phys Script, 31, 415–418.
Newell, A. C. (1985). Solitons in mathematics and physics, Soc for Ind and Appl Maths, Philadelphia.
Noguchi, A. (1974) Solitons in a nonlinear transmission line. Elec and Commun Japan. 57A, 9–13.
Ostrovskii, L. A and Papko, V. V. (1972) Solitary electromagenetic waves in nonlinear lines. Radiophysics, 15, 438–446.
Paulus, P. Wedding, B. Gasch, A. and Jäger, D. (1984) Bistability and solitons observed in a nonlinear ring resonator. Phys Lett, 102A, 89–92.
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.
Sakai, J. and Kawata, T. (1976) Nonlinear wave modulation in the transmission line. J Phys Soc Japan, 41, 1819–1820.
Scott, A. C. (1970) Active and nonlinear wave propagation in electronics. Wiley Interscience, New York.
Spatschek, K. H. (1978). Coupled localized electron-plasma waves and oscillatory ion-acoustic perturbations, Phys Fluids, 21, 1032–1035.
Suzuki, K. Hirota and Yoshikawa, K. (1973) The properties of phase modulated soliton trains. Jap J Appl Phys, 12, 361–365.
Suzuki, K. Hirota, R. and Yoshikawa, K. (1973) Amplitude modulated soliton trains and coding-decoding applications. Int J Electron, 34, 777.
Takagi, K. (1983) The power spectrum of a white noise passed through a nonlinear transmisión line. Jpn J Appl Phys. 22, 1466.
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.
Taniuti, T. and Yajima, N. (1969) Perturbation method for a nonlinear wave modulation. J Math Phys, 10, 1369–1372
Toda, M (1967) Vibrations of a chain with nonlinear interaction. J Phys Soc Japan, 22, 431–436.
Toda, M. (1970) Waves in nonlinear lattice. Prog Theor Phys Japan Suppl. 45, 174–201.
Watanabe, S. (1982) Solitons in nonlinear transmission line. J Phys Soc Japan, 51, 1030–1036.
Watanabe, S. Miyakawa, M. and Muroya, K. (1980) Experiment on recurrence in nonlinear LC circuit. J Phys Soc Japan, 48, 825–831.
Watanabe, S. Miyakawa, M. and Toda, M. (1978) Asymptotic behavior of collisionless shock in nonlinear LC circuit. J Phys Soc Japan, 45, 2030.
Yagi, T and Noguchi, A. (1977) Gyromagnetic nonlinear element and its application as a pulse-shaping transmission line. Electron Letters, 13, 683–685.
Yagi, T. and Noguchi, A. (1976) Experimental studies on modulational instability by using nonlinear transmission lines. Elec and Commun in Japan, 59A, 1–6.
Yazaki, T and Fukushima, K. (1985) Experimental studies of potential problems in quantum mechanics. Am J Phys, 53, 1186–1191.
Yoshinaga, T. and Kakutani, T. (1980) Solitary and shock waves on a coupled transmission line. J Phys Soc Japan, 49, 2072–2074.
Yoshinaga, T. and Kakutani, T. (1984) Second order KDV soliton on a nonlinear transmission line, J Phys Soc Japan, 53, 85–92.
Yoshinaga, T.Sugimoto, N and Kakutani, T. (1981) Nonlinear wave interactions on a discrete transmission line; J. Phys Soc Japan, 50, 2122–2128.
Section 2:Chapter
Barone, A. and Paterno, G. (1982) Physics and application of the Josephson effect. Wiley, New York.
Chen, J. T. Finnegan, T. F. and Langenberg, D. N. (1971) Physica 55, 413.
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.
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.
Davidson, A. Ducholm, B. and Pedersen, N. F. (1986) Experiments on soliton motion in annular Josephson Junctions. J. Appl. Phys., 60, 1447–1454.
Feyman, R.P. (1960) Lectures on Physics, Vol. 3 section 21.9. Addison Wesley, New York.
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.
Fulton, T. A. Magerlein, J. H. and Dynes, R. C. (1976) A Josephson logic design employing current switching junctions. AS 76, 56.
Harris, R. E. (1974) Cosine and other terms in the Josephson tunneling current. Phys. Rev. B. 10, 84–94.
Josephson, B. D. (1962) Possible new effects in superconductor tunneling. Phys. Lett. 1, 251–253.
Josephson, B. D. (1965) Supercurrents through barriers. Adv. Phys. 14, 419–451. see also (1964) Coupled superconductors. Rev Mod Phys, 36, 216–220.
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.
Likharev. K. K. (1986) Dynamics of Josephson junctions and circuits. Gordon and Breach, New York.
Lomdahl, P. S. (1985) Solitons in Josephson junctions: an overview, J Stat Phys, 39, 5/6, 551–561.
Lomsdahl, P. S. Soerensen, O. H. and Christiansen, P. L. (1982). Soliton excitations in Josephson tunnel junctions. Phys Rev. B, 25, 5737–5748.
Matsuda, A and Kawakami, T. (1983) Fluxon propagation on a Josephson Transmission line. Phys. Rev. Lett., 51, 695–697.
Matsuda, A. (1986) Observation of fluxon-antifluxon collision in a Josephson transmission line. Phys. Rev. B, 34, 3127–3135.
Matsuda, A. and Uheara, S. (1982) Observation of fluxon propagation on Josephson transmission line. Appl. Phys. Lett., 41, 770–772.
Me Laughlin, D. W. and Scott, A. C. (1978) Perturbation analysis of fluxon motion. Phys. Rev. A, 18, 1652–1680.
Nitta, J. Matsuda, A and Kawakami, T. (1984) Propagation properties of fluxons in a well damped Josephson transmission line. 55, 2758–2762.
Pagano, S. (1987) Nonlinear dynamics in long Josephson junctions, PhD Thesis, Technical Univ of Denmark, Lingby, Denmark.
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.
Pedersen, N. F and Welner, D. (1984) Comparison between experiments and perturbation theory for solitons in Josephson junctions. Phys. Rev. B, 29, 2551.
Pedersen, N. F. (1989) Nonlinear properties of Josephson Junctions. Proceedings of the ASI Summerschool on superconducting electronics, Ciccio, Italy Plenum.
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.
Pedersen, N. F. Samuelsen, M. R. and Welner, D. (1984) Soliton annhilation in the perturbed Sine Gordon system, Phys. Rev. B, 30, 4057–4059.
Scott, A. C. (1964) Distributed device application of the superconducting tunnel junction. Solid State Elee 7, 137–146.
Scott, A. C. (1969) A nonlinear Klein-Gordon equation, Am J Phys, 37, 52–61.
Swihart, J. C. (1961). Field solution for a thin film superconducting strip line. J. Appl. Phys. 32 461–469.
Section 3:Chapter
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.
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.
Blow, J. and Doran, N. J.(1987) Nonlinear effects in optical fibres and fibre devices. IEEE Proc, 134, 138–144.
Blow, K. J. and Doran, N. J. (1985) The asymptotic dispersion of soliton pulses in lossy fibres. Opt Commun, 52, 367–370.
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.
Cotter, D. (1982) Observation of stimulated Brillouin scattering in low loss silica fiber at 1.3μ m. Electron Lett., 18, 495–496.
Cotter, D. (1982) Transient stimulated Brillouin scattering in long single mode fibers. Electron Lett., 18, 504–506.
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.
Doran, N. J and Blow, K. J. (1983). Solitons in optical communications. IEEE J Qant Electron. QE-19, 1883–1888.
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.
Gloge, D. (1979) The optical fiber as a transmission medium. Rep Prog Phys, 42, 1777–1824.
Hasegawa, A. and Brinkman, W. F.(1980) Tunable coherent IR and FIR sources utilizing modulational instability. IEEE J. Quant Electron, QE-16, 694–697.
Hasegawa, A.(1983) Amplification and reshaping of optical soliton in a glass fiber. 4 Use of stimulated Raman process. Opt. Lett. 8, 650.
Hasegawa, A. (1984) Generation of a train of soliton pulses by induced modulational instability in optical fibers. Opt. Lett, 9, 288290.
Hasegawa, A. and Kodama, Y. (1981) Signal transmission by optical solitons in monomode fiber. Proc. IEEE, 69, 1145–1150.
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.
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.
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.
Jain, M. and Tzoar, N.(1987) Nonlinear pulse propagation in a monomode dielectric guide. IEEE J Qant Elec, QE-23, 510.
Kaminov, I. P. (1981) Polarization in optical fibers. IEEE Qant Elec, QE-17, 15–22.
Karpman, V. I. (1975), Nonlinear wave in dispersive media. Pergamon Press, NewYork.
Kodama, Y. (1985) Optical solitons in a monomode fiber. J Phys Stat, 39, 5/6, 597–614.
Kodama, Y. and Ablowitz, M. J. (1980) Perturbations of solitons and solitary waves. Stud. Appl. Math, 64, 225–245.
Kodama, Y. and Hasegawa, A. (1987) Nonlinear pulse propagation in a monomode dielectric guide. IEEE J Quant Elec. QE-23, 510–524.
Krokel, D. Halas, N. J. Gianlani, G and Grischowsky, D. (1988) dark pulse propagation in optical fibers. Phys Rev Lett, 60, 29–32.
Menyuk, C.R. (1987a) Nonlinear pulse propagation in birefringent optical fibers. IEEE J. Quant. Electron, QE-23, 174–176.
Menyuk, C. R. (1987b) Stability of solitons in birefringent optical fibers. I. equal propagation amplitudes. Opt Lett, 12, 614–616
Menyuk, C. R. (1988) Stability of solitons in birefringent optical fibers. II Arbitrary amplitudes. Opt Lett., 5, 392–402.
Mitscke, F. M. and Mollenauer, L. F. (1986) Discovery of the soliton self frequency shift. Opt. Lett, 11, 659–661.
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.
Mollenauer, L. F. and Stolen, R. H. (1984) The soliton laser. Opt lett. 9, 13.
Mollenauer, L. F. and Stolen, R. H. (1982) Solitons in optical fibers. Fiberoptic Technology, April, 193–198.
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.
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.
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.
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.
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.
Stegeman, G. I. and Stolen, R. H. (1988) Eds. Nonlinear guided wave phenomena in Optical Physics »Special issue, J Opt Soc Am B, 5.
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.
Tai, K. Hasegawa, A. and Tomita, A. (1986) Observation of modulation instability in optical fibers. Phys. Rev. Lett., 56, 135–138.
Taniuti, T. (1974) Reductive perturbative method and far fields of wave equations. Phys. Theor. Phys. (Japan), Suppl. 55, 1.
Tratruk, M. V. and Sipe, J. E. (1988) Bound solitary waves in a birefringent optical fiber. Phys. Rev. A 38, 2011–2017.
Wabnitz, C. R. (1988) Modulational polarization instability of light in a nonlinear birefringent dispersive medium. Phys. Rev. A, 38, 2018–2021.
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.
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.
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.
Zhakarov, V. E. and Shabat, A. B. (1973) Interaction between solitons in a stable medium. Sov. Phys. JETP, 37, 823–828.
Zhao, Wand Bourkoff, E. (1988) Femtosecond pulse propagation in optical fibers: higher order effects. IEEE J. Quant Electron., 24, 365–372.
Section 4:Chapter
Balakrishnan, R. and Bishop, A. R. (1985) Nonlinear Excitations on a quantum ferromagnetic chain. Phys Rev Lett, 55, 537–540.
Balucani, U. Lovesey, S. W., Rasetti, M. G. and Tognetti, V. Eds. (1984) Magnetic excitations and fluctuations. Springer Proceedings in Physics. Springer Verlag_Berlin.
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.
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.
Birgeneau, R. J. and Shirane, G (1978). Magnetism in one dimension. Physics Today, 32, Dec.
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.
Boucher, J. P. (1980)Solid State Commun, 33, 1025.
Boucher, J. P. (1989). Nonlinear excitations in antiferromagnetic chains. To be published in Proceedings of Nuclear in magnetism. Munich, August 1988.
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.
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.
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.
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.
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.
Cieplak, M. and Turski, L. A. (1980) Solitons in quantum Heisenberg chain. J Phys C, 13, 5741–5747.
Corones, J. (1977) Solitons as nonlinear magnons. Phys Rev B, 16, 1763–1764.
Cowley, R. A., Buyers, W. L. Martel, P. and Stevenson, R. W. (1969) Two magnon scattering of neutrons. Phys Rev Lett, 23, 86–89.
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.
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.
Fogedby, H. C. (1980) Solitons and magnons in the classical Heisenberg chain. J Phys A, 13, 1467–1499.
Gouvea, M. E and Pires, A, S. (1986) Nonlinear excitations in the classical one-dimensional antiferromagnet. Phys Rev B, 34, 306–317.
Izyumov, Y. A. (1989) Solitons in quasi one dimensional magnetic materials and their study by neutron scattering. Sov Phys Usp, to be published.
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.
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.
Kumar, P. (1982) Soliton instability in one-dimensional magnet. Phys. Rev. B 25, 483–486.
Laksmanan, M. (1977) Heisenberg continuum system as an exactly solvable dynamical system. Phys Lett, 53, 53–54.
Lindgärd, P. A. (1984), p 163, in Condensed Matter research using neutrons. Eds S. W. Lovesey and R. Scherm. Nato ASI series. Plenum, NewYork.
Magyari, E and Thomas, H. (1982) Kink instability in planar ferromagnets. Phys. Rev. B, 25, 531–533.
Makankov, V. G. and Fedyanin, V. K. (1984) Nonlinear effects in quasi-one-dimensional models of condensed matter theory. Phys Rep, 104, 1–86.
Maki, K. (1980) Quantum statistics of solitons, p 63 in Physics in one dimension. Eds Bernasconi, J. and Schneider, T. Springer, Berlin.
Maki, K.(1981) Quantum effects in quasi-one dimensional magnetic systems. Phys Rev B, 24, 3991–332.
Mikeska, H. J. (1981) Solitons in one dimensional ferromagnets. J. Appl. Phys., 52, 1950–1955.
Mikeska, H. J. (1982) Soliton energy in an easy plane quantum spin chain. Phys Rev B, 26, 5213–5222.
Mikeska, H. J. (1978) Solitons in one-dimensional magnet whith an easy plane. J. Phys. C 11, L29–L32.
Mikeska, H. J. (1980) Nonlinear dynamics of classical one dimensional ferromagnets. J. Phys. C, 13, 2913–2923.
Ramirez, A. P. and wolf, W, P. (1982) Specific of CsNiF3: evidence for spin solitons. Phys Rev Lett, 49, 227–229.
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.
Remoissenet, M. (1986). Lowamplitude breather and envelope solitons in quasi-one-dimensional physical models. Phys Rev B, 33, 2386–2392.
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.
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.
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.
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.
Tjon, J. and Wright, J. (1977) Solitons in the continuous Heisenberg chain. Phys Rev B, 15, 3470–3476.
Villain, J. (1975) Physica. Propagative spin relaxation in the Ising-like antiferromagnetic linear chain. 79B, 1–12.
Wysin, G and Kumar, P. (1987) Thermomagnetic transport coefficients: solitons in an easy plane magnetic chain. Phys Rev B, 13, 7063–7070.
Wysin, G. Bishop, A. R and Kumar, P. (1982) Solitons dynamics on a ferromagnetic chain. J. Phys. C, 15, L337–L344.
Wysin, G. Bishop, A. R and Kumar, P. (1984) Soliton dynamics on an easy plane ferromagnetic chain J. Phys. C, 17, 5975–5992.
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.
Zhakarov, V. E. and Schulman, E.I. (1982) To the integrability of the system of two coupled nonlinear Schrödinger squations. Physica 4D, 270–274.
Section 5:Chapter
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.
Balanowski, E. and Beaconsfield, P. (1985). Solitonlike excitations in biological systems. Phys. Rev. A, 32, 3059–3064.
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.
Barthés, M. (1989) Optical anomalies in acetanalide Davydov solitons, localised modes or Fermi resonance ? To be published in J Mol Liq, special issue.
Baverstock, K. F. and Cundall, R. B. (1988). Solitons and energy transfer in DNA. Nature, 322, March 24, 312–313.
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.
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.
Davydov, A. S. (1985). Solitons in Molecular Systems, Reidel, Dordrecht.
Del Giudice, Doglia, S. and Milani, M. (1982) A collective dynamics in metabolically active cells. Phys Script, 26, 232–238.
Dickerson, R. E. (1983). The DNA helix and howit is read. Sci Amer, December, 87–104.
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.
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.
Freifelder, D. (1987). Molecular biology. Jones and Bartlett, Publishers, Boston.
Friedland, P. and Kedes, L. H. (1985) Discovering the secrets of DNA. Commun of ACM, 28, 1164–1186.
Fröhlich, H (1969), Quantum mechanical concepts in biology, p 13 in Theoretical Physics and Biology, Eds Marois, North Holland, Amsterdam.
Fröhlich, H. (1968). Long range coherence and energy storage in biological systems. Int J Quant Chern, II, 641–649.
Heeger, A. J, Kivelson, S, Schrieffer J. R. and Su, W. P. (1988) Solitons in conducting polymers. Rev Mod Phys, 60, 781–850.
Homma, S and Takeno, S. (1984). A coupled base-rotator model for structure and dynamics of DNA, Prog Theor Phys, 72, 679–693.
Hyman, J. M. Mc Laughlin, D.W. and Scott, A. C. (1981). On Davydov’s a- Helix solitons. Physica D, 3D, 23.
Kim, Y. and Prohofsky, E. W. (1987). Vibrational modes of a DNA polymer at low temperature. Phys. Rev. B, 36, 3449–3451.
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.
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.
Lewitt, M. (1982). Computer Simulation of DNA Double-helix dynamics Cold Spring Harbor Symp Quant Biol, 46A, 251–262.
Lilley, D. M. (1988). DNA opens up, supercoiling and heavy breathing, TIG, 4, 111–121.
Lomdahl, P.S. Layne, S.P. and Bigio, I. J. Solitons in biology (1985). Los Alamos Sciences, Spring Issue, 4–21.
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.
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.
Muto, V. Halding, J. Christiansen P. L. and Scott, A. C. (1988) Solitons in DNA. J Biomol Struct and Dyn, 5, 873–874.
Muto, V. Scott, A. C. and Christiansen, P. L. (1989). Thermally generated solitons in DNA. Preprint
Peyrard, M. and Bishop, A. R. (1989) Statistical mechanics of a nonlinear model for DNA denaturation. Preprint.
Prohofsky, E. W. (1988) Solitons hiding in DNA and their possible significance in RNA transcription. Phys Rev B, 38, 1538–1554.
Saenger, W. (1984). Principles of nucleic acid structure, Springer, NewYork.
Scott, A. C. (1982a). Dynamics of Davydov solitons. Phys. Rev. B, 26, 578–595.
Scott, A. C. (1982b) The vibrational structure of Davydov soliton. Phys. Script. 35, 651–672.
Scott, A. C. (1985a). Solitons in biological molecules. Comments Moll. Cell. Biophys., 3, 15–37.
Scott, A. C. (1985b). Soliton oscillations in DNA, Phys Rev A, 31, 3518–3519.
Scott, A.C.(1985c). Anharmonic analysis of resonant microwave absorption in DNA, Phys Script, 36, 617–638.
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.
Szent-Giörgyi, A. (1941) The study of energy levels in biochemistry. Nature, 148, 157–159.
Takeno, S. and Homma, S. (1987). Kinks and breathers associated with collective sugar puckering in DNA. Prog. Theor. Phys. 77, 548–562.
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.
Wang, X. Brown, D. W. and Linenberg, K. (1989) Quantum Monte Carlo simulation of the Davydov model. Phys Rev Lett, 1796–1799.
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.
Yomosa, S. (1983). Soliton excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. A, 27, 2120–2125.
Yomosa, S. (1984). Solitary excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. A, 30, 474–480.
Zhakarov, V.E. (1972). Collapse of Langmuir waves. Sov. Phys. JETP, 72, 908–919.
Zhang, G. (1987) Soliton excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. II, 35, 886–891.
Ziman, J. Electrons and phonons: the theory of transport phenomena in Solids. Clarendon, Oxford, 1980
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Remoissenet, M. (1990). Nonlinear Evolution Equations, Quasi-Solitons and their Experimental Manifestation. In: Conte, R., Boccara, N. (eds) Partially Intergrable Evolution Equations in Physics. NATO ASI Series, vol 310. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0591-7_6
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