Nonlocal Modified KdV Equations and Their Soliton Solutions

Metin Gürses; Aslı Pekcan

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arXiv · 1711.01588

Nonlocal Modified KdV Equations and Their Soliton Solutions

Metin Gürses·Aslı Pekcan

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Abstract

We study the nonlocal modified Korteweg-de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz-Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota direct method. Then by using the Ablowitz-Musslimani reduction formulas, we find one-, two-, and three-soliton solutions of local and nonlocal complex mKdV and mKdV equations. The soliton solutions of these equations are of two types. We give one-soliton solutions of both types and present only first type of two- and three-soliton solutions. We illustrate our soliton solutions by plotting their graphs for particular values of the parameters.

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Metin Gürses, Aslı Pekcan. 2017-11-05. Nonlocal Modified KdV Equations and Their Soliton Solutions. https://arxiv.org/abs/1711.01588

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