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Yayın 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, IrmaIn 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.Yayın Global existence and nonexistence results for a generalized Davey-Stewartson system(IOP Publishing, 2004-12-03) Babaoğlu, Ceni; Eden, Osman Alp; Erbay, SaadetWe consider a system of three equations, which will be called generalized Davey-Stewartson equations, involving three coupled equations, two for the long waves and one for the short wave propagating in an infinite elastic medium. We classify the system according to the signs of the parameters. Conserved quantities related to mass, momentum and energy are derived as well as a specific instance of the so-called virial theorem. Using these conservation laws and the virial theorem both global existence and nonexistence results are established under different constraints on the parameters in the elliptic-elliptic-elliptic case.
