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A sixth-order nonlinear Schrödinger equation as a reduction of the nonlinear Klein–Gordon equation for slowly modulated wave trains

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Abstract

We use the method of multiple scales to derive a sixth-order nonlinear Schrödinger equation governing the evolution of slowly modulated plane-wave solutions to the nonlinear Klein–Gordon equation with polynomial nonlinearity. The coefficients of this sixth-order equation are expressed explicitly in terms of the velocity parameter as well as linear, quadratic, cubic, quadruple, and quintic nonlinear coefficients of the original nonlinear Klein–Gordon equation.

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Authors and Affiliations

  1. Institute of Physics, National Academy of Sciences of Ukraine, Prosp. Nauky 46, Kyiv, 03028, Ukraine

    Yuri V. Sedletsky & Ivan S. Gandzha

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  1. Yuri V. Sedletsky
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  2. Ivan S. Gandzha
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Correspondence to Ivan S. Gandzha.

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This paper is dedicated to the blessed memory of Dr. V. P. Lukomsky (14.01.1942—31.03.2008).

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Sedletsky, Y.V., Gandzha, I.S. A sixth-order nonlinear Schrödinger equation as a reduction of the nonlinear Klein–Gordon equation for slowly modulated wave trains. Nonlinear Dyn 94, 1921–1932 (2018). https://doi.org/10.1007/s11071-018-4465-x

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