Reducing a generalized Davey-Stewartson system to a non-local nonlinear Schrodinger equation


Eden A., Erbay S., Hacınlıyan İ.

CHAOS SOLITONS & FRACTALS, vol.41, no.2, pp.688-697, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.1016/j.chaos.2007.11.035
  • Journal Name: CHAOS SOLITONS & FRACTALS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.688-697
  • Istanbul Technical University Affiliated: Yes

Abstract

In the present study, we consider a generalized (2 + 1) Davey-Stewartson (GDS) system consisting of a nonlinear Schrodinger (NLS) type equation for the complex amplitude of a short wave and two asymmetrically coupled linear wave equations for long waves propagating in an infinite elastic medium. We obtain integral representation of solutions to the coupled linear wave equations and reduce the GDS system to a NLS equation with non-local terms. Finally, we present localized solutions to the GDS system, decaying in both spatial coordinates, for a special choice of parameters by using the integral representation of solutions to the coupled linear wave equations. (C) 2008 Elsevier Ltd. All rights reserved.