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Quasilinear theory for the nonlinear Schrödinger equation with periodic coefficients

  • Nonlinear Dynamics
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Abstract

The nonlinear Schrödinger equation with periodic coefficients is analyzed under the condition of large variation in the local dispersion. The solution after n periods is represented as the sum of the solution to the linear part of the nonlinear Schrödinger equation and the nonlinear first-period correction multiplied by the number of periods n. An algorithm for calculating the quasilinear solution with arbitrary initial conditions is proposed. The nonlinear correction to the solution for a sequence of Gaussian pulses is obtained in the explicit form.

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Authors and Affiliations

  1. Institute of Computational Technologies, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 6, Novosibirsk, 630090, Russia

    S. B. Medvedev & M. P. Fedoruk

Authors
  1. S. B. Medvedev
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  2. M. P. Fedoruk
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Translated from Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 79, No. 1, 2004, pp. 19–24.

Original Russian Text Copyright © 2004 by Medvedev, Fedoruk.

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Medvedev, S.B., Fedoruk, M.P. Quasilinear theory for the nonlinear Schrödinger equation with periodic coefficients. Jetp Lett. 79, 16–20 (2004). https://doi.org/10.1134/1.1675913

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  • DOI: https://doi.org/10.1134/1.1675913

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