English

Nonlocal Modified KdV Equations and Their Soliton Solutions

Exactly Solvable and Integrable Systems 2017-11-28 v2

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.

Keywords

Cite

@article{arxiv.1711.01588,
  title  = {Nonlocal Modified KdV Equations and Their Soliton Solutions},
  author = {Metin Gürses and Aslı Pekcan},
  journal= {arXiv preprint arXiv:1711.01588},
  year   = {2017}
}

Comments

52 pages, 33 figures

R2 v1 2026-06-22T22:36:25.375Z