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

Alp Eden; Saadet Erbay; Irma Hacinliyan

doi:10.1016/j.chaos.2007.11.035

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

Alp Eden
, Saadet Erbay
, Irma Hacinliyan^*

^*Corresponding author for this work

Department of Mathematics Engineering

Bogazici University
Scientific and Technological Research Council of Turkey
Isik University

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In the present study, we consider a generalized (2 + 1) Davey-Stewartson (GDS) system consisting of a nonlinear Schrödinger (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.

Original language	English
Pages (from-to)	688-697
Number of pages	10
Journal	Chaos, Solitons and Fractals
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/j.chaos.2007.11.035
Publication status	Published - 30 Jul 2009

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10.1016/j.chaos.2007.11.035

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abstract = "In the present study, we consider a generalized (2 + 1) Davey-Stewartson (GDS) system consisting of a nonlinear Schr{\"o}dinger (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.",

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AU - Eden, Alp

AU - Erbay, Saadet

AU - Hacinliyan, Irma

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Y1 - 2009/7/30

N2 - In the present study, we consider a generalized (2 + 1) Davey-Stewartson (GDS) system consisting of a nonlinear Schrödinger (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.

AB - In the present study, we consider a generalized (2 + 1) Davey-Stewartson (GDS) system consisting of a nonlinear Schrödinger (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.

UR - https://www.scopus.com/pages/publications/67349230622

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JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 2

ER -

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

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