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Analysis of Some Properties of the Nonlinear Schrödinger Equation Used for Filamentation Modeling

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Properties of the integral of motion and evolution of the effective light beam radius are analyzed for the stationary model of the nonlinear Schrödinger equation describing the filamentation. It is demonstrated that within the limits of such model, filamentation is limited only by the dissipation mechanisms.

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References

  1. L. A. Takhtadzhyan and L. D. Faddeev, Hamiltonian Approach in the Theory of Solitons [in Russian], Nauka, Moscow (1986).

  2. S. N. Vlasov and V. I. Talanov, Self-Focusing of Waves [in Russian], Institute of Applied Physics RAS, Nizhny Novgorod (1997).

  3. A. V. Shapovalov, A. Yu. Trifonov, and A. L. Lisok, Symmetry Integr. Geom., 1, 007 (2005).

    Google Scholar 

  4. A. V. Shapovalov, A. Yu. Trifonov, and A. L. Lisok, J. Phys. Conf. Ser., 670, 012046 (2016).

  5. R. W. Boyd et al., eds., Self-Focusing: Past and Present. Fundamentals and Prospects, Topics in Applied Physics, Vol. 114, Springer, Berlin (2009), pp. 3–19.

  6. K. D. Moll, A. E. Gaeta, and G. Fibich, Phys Rev. Lett., 90, No. 20, 203902 (2003).

    Article  ADS  Google Scholar 

  7. V. N. Alekseenko, Differ. Equat., 12, No. 6, 1121–1122 (1976).

    Google Scholar 

  8. W. Ettoumi, J. Kasparian, and J.-P. Wolf, Phys. Rev. Lett., 114, No. 6, 063903 (2015).

  9. L. Berge and A. Couairon, Physica D, 152–153, 752–762 (2001).

    Article  Google Scholar 

  10. S. V. Chekalin and V. P. Kandidov, Usp. Fiz. Nauk, 183, 133–152 (2013).

    Article  Google Scholar 

  11. N. Akozbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E, 61, No. 4, 4540–4549 (2000).

    Article  ADS  Google Scholar 

  12. L. L. Tatarinova and M. E. Garcia, Physica D, 240, Nos. 9–10, 894–901 (2011).

    Article  ADS  Google Scholar 

  13. A. A. Zemlyanov, A. D. Bulygin, and Yu. È. Geints, Opt. Atmos. Okeana, 24, No. 10, 839–847 (2011).

    Google Scholar 

  14. Yu. E. Geints, A. D. Bulygin, and A. A. Zemlyanov, Appl. Phys. B, 107, No. 1, 243–255 (2012).

    Article  ADS  Google Scholar 

  15. A. A. Zemlyanov and Yu. É. Geints, Opt. Atmos. Okeana, 18, No. 07, 574–579 (2005).

    Google Scholar 

  16. A. D. Bulygin and. A. A. Zemlyanov, Vychisl. Tekhnol., 22, No. 5, 3 (2017).

  17. V. E. Zakharov et al., Zh. Eksp. Teor. Fiz., 60, No. 1, 136 (1971).

  18. A. D. Balashov and A. Kh. Pergament, Matem. Model., 18, No. 4, 3 (2006).

    Google Scholar 

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Authors and Affiliations

  1. V. E. Zuev Institute of Atmospheric Optics of the Siberian Branch of the Russian Academy of Sciences, Tomsk, Russia

    A. A. Zemlyanov & A. D. Bulygin

Authors
  1. A. A. Zemlyanov
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  2. A. D. Bulygin
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Correspondence to A. A. Zemlyanov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 136–141, February, 2018.

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Zemlyanov, A.A., Bulygin, A.D. Analysis of Some Properties of the Nonlinear Schrödinger Equation Used for Filamentation Modeling. Russ Phys J 61, 357–363 (2018). https://doi.org/10.1007/s11182-018-1407-5

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  • DOI: https://doi.org/10.1007/s11182-018-1407-5

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