Nonlocal modified KdV equations and their soliton solutions by Hirota Method

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GÜRSES M., Pekcan A.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.67, pp.427-448, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67
  • Publication Date: 2019
  • Doi Number: 10.1016/j.cnsns.2018.07.013
  • Journal Name: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.427-448
  • Keywords: Ablowitz-Musslimani reduction, Nonlocal mKdV equations, Hirota bilinear form, Soliton solutions, DE-VRIES EQUATION, INVERSE SCATTERING TRANSFORM
  • Hacettepe University Affiliated: Yes

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 nonlocal mKdV and nonlocal complex 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 solutions by plotting their graphs for particular values of the parameters. (C) 2018 Elsevier B.V. All rights reserved.