TY - JOUR
T1 - Reducing a generalized Davey-Stewartson system to a non-local nonlinear Schrödinger equation
AU - Eden, Alp
AU - Erbay, Saadet
AU - Hacinliyan, Irma
PY - 2009/7/30
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 - http://www.scopus.com/inward/record.url?scp=67349230622&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2007.11.035
DO - 10.1016/j.chaos.2007.11.035
M3 - Article
AN - SCOPUS:67349230622
SN - 0960-0779
VL - 41
SP - 688
EP - 697
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 2
ER -