(2+1)-dimensional local and nonlocal reductions of the negative AKNS system: Soliton solutions


GÜRSES M., Pekcan A.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.71, pp.161-173, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71
  • Publication Date: 2019
  • Doi Number: 10.1016/j.cnsns.2018.11.016
  • Title of Journal : COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Page Numbers: pp.161-173
  • Keywords: Ablowitz-Musslimani reduction, (2+1)-dimensional negative AKNS hierarchy, Hirota bilinear method, Soliton solutions, INVERSE SCATTERING TRANSFORM, DE-VRIES EQUATION, REPRESENTATIONS

Abstract

We first construct a (2 + 1)-dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear forms of the negative AKNS hierarchy and give one- and two-soliton solutions. By using the soliton solutions of the negative AKNS hierarchy we find one-soliton solutions of the local and nonlocal reduced equations. (C) 2018 Elsevier B.V. All rights reserved.