Işık Üniversitesi Kurumsal Akademik Belleği :: DSpace Angular

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Standing waves for a generalized Davey-Stewartson system
(IOP Publishing, 2006-10-27) Eden, Osman Alp; Erbay, Saadet
In this paper, we establish the existence of non-trivial solutions for a semi-linear elliptic partial differential equation with a non-local term. This result allows us to prove the existence of standing wave ( ground state) solutions for a generalized Davey-Stewartson system. A sharp upper bound is also obtained on the size of the initial values for which solutions exist globally.
Reducing a generalized Davey-Stewartson system to a non-local nonlinear Schrodinger equation
(Pergamon-Elsevier Science Ltd, 2009-07-30) Eden, Osman Alp; Erbay, Saadet; Hacınlıyan, Irma
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.