Nonlocal Modified KdV Equations and Their Soliton Solutions

2017/11/05 by Metin Gürses, Gürses, Metin, Aslı Pekcan +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1711.01588

openalex publication_date 2017/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Integrable Nonlocal Nonlinear Equations
• Nonlocal Super Integrable Equations
• Transformations between nonlocal and local integrable equations
• Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence

Cited by

• Painlevé Integrability And Shifted Nonlocal Reductions Of A Variable Coefficient Coupled HI Mkdv System

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