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Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

  • Atoms, Molecules, Optics
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Abstract

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.

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References

  1. H. Leblond and D. Mihalache, Phys. Rep. 523, 61 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  2. A. I. Maimistov, Quantum Electron. 30, 287 (2000).

    Article  ADS  Google Scholar 

  3. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Nauka, Moscow, 1988; Amer. Inst. Phys., Bristol, 1992).

    Google Scholar 

  4. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).

    Article  ADS  Google Scholar 

  5. K. Nakamura and M. Nakazawa, Opt. Lett. 21, 68 (1996).

    Article  ADS  Google Scholar 

  6. F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009).

    Article  ADS  Google Scholar 

  7. G. Kh. Kitaeva, Laser Phys. Lett. 5, 559 (2008).

    Article  ADS  Google Scholar 

  8. S. V. Sazonov, JETP Lett. 96, 263 (2012).

    Article  ADS  Google Scholar 

  9. IEEE Trans. Terahertz Sci. Technol. 1 (2) (2011).

  10. P. G. Kryukov, Femtosecond Pulses: Introduction into a New Area of Laser Physics (Fizmatlit, Moscow, 2008) [in Russian].

    Google Scholar 

  11. S. V. Sazonov, J. Exp. Theor. Phys. 119, 423 (2014).

    Article  Google Scholar 

  12. S. A. Kozlov and S. V. Sazonov, J. Exp. Theor. Phys. 84, 332 (1997).

    Google Scholar 

  13. S. V. Sazonov, J. Exp. Theor. Phys. 92, 361 (2001).

    Article  ADS  Google Scholar 

  14. H. Leblond, S. V. Sazonov, I. V. Mel’nikov, D. Mihalache, and F. Sanchez, Phys. Rev. A 74, 063815 (2006).

    Article  ADS  Google Scholar 

  15. L. W. Casperson, Phys. Rev. A 57, 609 (1998).

    Article  ADS  Google Scholar 

  16. A. Brown, W. J. Meath, and P. Tran, Phys. Rev. A 63, 013403 (2000).

    Article  ADS  Google Scholar 

  17. M. Agrotis, N. M. Ercolani, S. A. Glasgow, and J. V. Moloney, Physica D 138, 134 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  18. A. A. Zabolotskii, J. Exp. Theor. Phys. 94, 869 (2002).

    Article  ADS  Google Scholar 

  19. A. I. Maimistov and J.-G. Capmuto, Opt. Spectrosc. 94, 245 (2003).

    Article  ADS  Google Scholar 

  20. S. V. Sazonov, J. Exp. Theor. Phys. 97, 722 (2003).

    Article  ADS  Google Scholar 

  21. S. V. Sazonov and N. V. Ustinov, J. Exp. Theor. Phys. 100, 256 (2005).

    Article  ADS  Google Scholar 

  22. S. O. Elyutin, J. Exp. Theor. Phys. 101, 11 (2005).

    Article  ADS  Google Scholar 

  23. S. V. Sazonov and N. V. Ustinov, Quantum Electron. 35, 701 (2005).

    Article  ADS  Google Scholar 

  24. S. V. Sazonov and N. V. Ustinov, JETP Lett. 83, 483 (2006); J. Exp. Theor. Phys. 103, 561 (2006).

    Article  ADS  Google Scholar 

  25. N. V. Ustinov, Proc. SPIE 6725, 67250F-1 (2007), arXiv:0705.2833.

    Google Scholar 

  26. S. V. Sazonov and N. V. Ustinov, Opt. Spectrosc. 106, 416 (2009).

    Article  ADS  Google Scholar 

  27. S. V. Sazonov and N. V. Ustinov, J. Exp. Theor. Phys. 115, 741 (2012).

    Article  ADS  Google Scholar 

  28. L. D. Faddeev, Phys. Usp. 56, 465 (2013).

    Article  ADS  Google Scholar 

  29. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method (Springer-Verlag, New York, 1984; Nauka, Moscow, 1980).

    MATH  Google Scholar 

  30. G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980; Mir, Moscow, 1983).

    MATH  Google Scholar 

  31. Solitons, Ed. by R. K. Bullough and P. J. Caudrey (Springer, Berlin, 1980; Mir, Moscow, 1983).

  32. R. K. Dodd, J. C. Eilbeck, J. D. Giddon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic Press, London, 1982; Mir, Moscow, 1988).

    Google Scholar 

  33. S. V. Sazonov, Opt. Commun. 380, 480 (2016).

    Article  ADS  Google Scholar 

  34. S. V. Sazonov and A. F. Sobolevskii, J. Exp. Theor. Phys. 96, 1019 (2003).

    Article  ADS  Google Scholar 

  35. E. M. Belenov and A. V. Nazarkin, JETP Lett. 51, 288 (1990).

    ADS  Google Scholar 

  36. E. M. Belenov, A. V. Nazarkin, and V. A. Ushchapovskii, Sov. Phys. JETP 73, 422 (1991).

    Google Scholar 

  37. I. I. Sobel’man, Introduction to the Theory of Atomic Spectra, International Series of Monographs in Natural Philosophy (Nauka, Moscow, 1977; Pergamon, Oxford, 1972).

    Google Scholar 

  38. A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics, 3rd ed. (Nauka, Moscow, 1981; Wiley, New York, 1965)

    Google Scholar 

  39. J. C. Eilbeck, J. D. Gibbon, P. J. Caudrey, and R. K. Bullough, J. Phys. A: Math. Gen. 6, 1337 (1973).

    Article  ADS  Google Scholar 

  40. M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory (Nauka, Moscow, 1979) [in Russian].

    MATH  Google Scholar 

  41. T. Schäfer and C. E. Wayne, Physica D 196, 90 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  42. Y. Chung, C. K. R. T. Jones, T. Schäfer, and C. E. Wayne, Nonlinearity 18, 1351 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  43. R. Beals, M. Rabelo, and K. Tenenblat, Stud. Appl. Math. 81, 125 (1989).

    Article  MathSciNet  Google Scholar 

  44. M. L. Rabelo, Stud. Appl. Math. 81, 221 (1989).

    Article  MathSciNet  Google Scholar 

  45. A. Sakovich and S. Sakovich, J. Phys. Soc. Jpn. 74, 239 (2005).

    Article  ADS  Google Scholar 

  46. Y. Matsuno, J. Math. Phys. 52, 123702 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  47. L. A. Ostrovskii, Okeanologiya 18, 181 (1978).

    Google Scholar 

  48. A. Boutet de Monvel and D. Shepelsky, J. Phys. A: Math. Theor. 48, 035204 (2015).

    Article  ADS  Google Scholar 

  49. J. Hunter, Lect. Appl. Math. 26, 301 (1990).

    ADS  Google Scholar 

  50. V. A. Vakhnenko, J. Phys. A: Math. Gen. 25, 4181 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  51. R. A. Kraenkel, H. Leblond, and M. A. Manna, J. Phys. A: Math. Theor. 47, 025208 (2014).

    Article  ADS  Google Scholar 

  52. S. V. Sazonov and N. V. Ustinov, JETP Lett. 99, 503 (2014).

    Article  ADS  Google Scholar 

  53. V. O. Vakhnenko and E. J. Parkes, Nonlinearity 11, 1457 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  54. A. J. Morrison, E. J. Parkes, and V. O. Vakhnenko, Nonlinearity 12, 1427 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  55. M. A. Manna and A. Neveu, Inverse Problems 17, 855 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  56. G. Tzitzéca, C. R. Acad. Sci. Paris 144, 1257 (1907).

    Google Scholar 

  57. R. K. Dodd and R. K. Bullough, Proc. R. Soc. London A 351, 499 (1976).

    Article  ADS  Google Scholar 

  58. A. V. Zhiber and A. B. Shabat, Sov. Phys. Dokl. 24, 607 (1979).

    ADS  Google Scholar 

  59. A. V. Mikhailov, JETP Lett. 30, 414 (1979).

    ADS  Google Scholar 

  60. V. O. Vakhnenko and E. J. Parkes, Chaos, Solitons, Fractals 13, 1819 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  61. A. N. W. Hone and J. P. Wang, Inverse Probl. 19, 129 (2003).

    Article  ADS  Google Scholar 

  62. A. Degasperis and M. Procesi, in Symmetry and Perturbation Theory, Ed. by A. Degasperis and G. Gaeta (World Scientific, Singapore, 1999), p. 22.

  63. A. Degasperis, A. N. W. Hone, and D. D. Holm, Theor. Math. Phys. 133, 1463 (2002).

    Article  Google Scholar 

  64. Y. Matsuno, Phys. Lett. A 359, 451 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  65. J. P. Boyd, Phys. Lett. A 338, 36 (2005).

    Article  ADS  Google Scholar 

  66. A. Stefanov, Y. Shen, and P. G. Kevrekidis, J. Diff. Eqs. 249, 2600 (2010).

    Article  ADS  Google Scholar 

  67. Y. Liu, D. Pelinovsky, and A. Sakovich, SIAM J. Math. Anal. 42, 1967 (2010).

    Article  MathSciNet  Google Scholar 

  68. R. H. J. Grimshaw, K. Helfrich, and E. R. Johnson, Stud. Appl. Math. 129, 414 (2012).

    Article  MathSciNet  Google Scholar 

  69. R. Grimshaw and D. Pelinovsky, Discrete Cont. Dyn. Syst., Ser. A 84, 559 (2013).

    Google Scholar 

  70. Y. A. Stepanyants, Chaos, Solitons, Fractals 28, 193 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  71. E. J. Parkes, Chaos, Solitons, Fractals 31, 602 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  72. A.-M. Wazwaz, Phys. Scripta 82, 065006 (2010).

    Article  ADS  Google Scholar 

  73. B.-F. Feng, K. Maruno, and Y. Ohta, J. Phys. A: Math. Theor. 45, 355203 (2012).

    Article  Google Scholar 

  74. Y. Ye, J. Song, S. Shen, and Y. Di, Results Phys. 2, 170 (2012).

    Article  ADS  Google Scholar 

  75. X. H. Liu and C. He, ISRN Math. Phys. 2013, 1 (2013).

    Article  ADS  Google Scholar 

  76. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer, Berlin, 1991).

    Book  MATH  Google Scholar 

  77. V. Varlamov and Y. Liu, Discrete Contin. Dyn. Syst. 10, 731 (2004).

    Article  MathSciNet  Google Scholar 

  78. G. Gui and Y. Liu, Comm. Partial Diff. Eqs. 32, 1895 (2007).

    Article  Google Scholar 

  79. A. Sakovich and S. Sakovich, J. Phys. A: Math. Gen. 39, L361 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  80. A. V. Mikhailov, Physica D 3, 73 (1981).

    Article  ADS  Google Scholar 

  81. A. Alias, R. H. J. Grimshaw, and K. R. Khusnutdinova, Chaos 23, 023121 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  82. K. R. Khusnutdinova, A. M. Samsonov, and A. S. Zakharov, Phys. Rev. E 79, 056606 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  83. K. R. Khusnutdinova and K. M. Moore, Wave Motion 48, 738 (2011).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. National Research Centre “Kurchatov Institute,”, Moscow, 123182, Russia

    S. V. Sazonov

  2. Kaliningrad Branch, Moscow State University of Railways, Kaliningrad, 236039, Russia

    N. V. Ustinov

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  1. S. V. Sazonov
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  2. N. V. Ustinov
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Correspondence to S. V. Sazonov.

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Original Russian Text © S.V. Sazonov, N.V. Ustinov, 2017, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 151, No. 2, pp. 249–269.

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Sazonov, S.V., Ustinov, N.V. Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules. J. Exp. Theor. Phys. 124, 213–230 (2017). https://doi.org/10.1134/S1063776117010150

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