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Standing waves for a generalized Davey-Stewartson system
(IOP Publishing, 2006-10-27)
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 ...
On travelling wave solutions of a generalized Davey-Stewartson system
(Oxford Univ Press, 2005-02)
The generalized Davey-Stewartson (GDS) equations, as derived by Babaoglu & Erbay (2004, Int. J. Non-Linear Mech., 39, 941-949), is a system of three coupled equations in (2 + 1) dimensions modelling wave propagation in an ...
Non-existence and existence of localized solitary waves for the two-dimensional long-wave-short-wave interaction equations
(Elsevier Ltd, 2010-04)
In this study, we establish the non-existence and existence results for the localized solitary waves of the two-dimensional long-wave-short-wave interaction equations. Both the non-existence and existence results are based ...
Two-dimensional wave packets in an elastic solid with couple stresses
(Pergamon-Elsevier Science Ltd, 2004-08)
The problem of (2+1) (two spatial and one temporal) dimensional wave propagation in a bulk medium composed of an elastic material with couple stresses is considered. The aim is to derive (2+1) non-linear model equations ...
Coupled quintic nonlinear Schrodinger equations in a generalized elastic solid
(IOP Publishing Ltd, 2004-10-08)
In the present study, the nonlinear modulation of transverse waves propagating in a cubically nonlinear dispersive elastic medium is studied using a multiscale expansion of wave solutions. It is found that the propagation ...
A higher-order model for transverse waves in a generalized elastic solid
(Pergamon-Elsevier Science, 2002-11)
In the present study, the nonlinear modulation of transverse waves propagating in a generalized elastic solid is studied using a multi-scale expansion of quasi-monochromatic wave solutions. In particular, to include the ...
Global existence and nonexistence results for a generalized Davey-Stewartson system
(IOP Publishing, 2004-12-03)
We 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 ...
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
(IOP Publishing Ltd, 2011-04)
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the ...
Reducing a generalized Davey-Stewartson system to a non-local nonlinear Schrodinger equation
(Pergamon-Elsevier Science Ltd, 2009-07-30)
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 ...
Stability of solitary waves for three-coupled long wave-short wave interaction equations
(Oxford Univ Press, 2011-08)
In this paper, we consider a three-component system of 1D long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions ...
