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Highly Dispersive Optical Solitons of an Equation with Arbitrary Refractive Index

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Abstract

A nonlinear fourth-order differential equation with arbitrary refractive index for description of the pulse propagation in an optical fiber is considered. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we look for solutions of the equation using the traveling wave reduction. We present a novel method for finding soliton solutions of nonlinear evolution equations. The essence of this method is based on the hypothesis about the possible type of an auxiliary equation with an already known solution. This new auxiliary equation is used as a basic equation to look for soliton solutions of the original equation. We have found three forms of soliton solutions of the equation at some constraints on parameters of the equation.

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Funding

This research was supported by the Russian Foundation for Basic Research according to the research project No. 18-29-10025.

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  1. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe sh. 31, 115409, Moscow, Russia

    Nikolay A. Kudryashov

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  1. Nikolay A. Kudryashov
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Correspondence to Nikolay A. Kudryashov.

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Kudryashov, N.A. Highly Dispersive Optical Solitons of an Equation with Arbitrary Refractive Index. Regul. Chaot. Dyn. 25, 537–543 (2020). https://doi.org/10.1134/S1560354720060039

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