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Yayın Standing waves for a generalized Davey-Stewartson system(IOP Publishing, 2006-10-27) Eden, Osman Alp; Erbay, SaadetIn 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.Yayın Numerical simulation of blow-up solutions for the generalized Davey-Stewartson system(Taylor & Francis Ltd, 2011-03) Muslu, Gülçin Mihriye; Erbay, Hüsnü AtaBlow-up solutions for the generalized Davey-Stewartson system are studied numerically by using a split-step Fourier method. The numerical method has spectral-order accuracy in space and first-order accuracy in time. To evaluate the ability of the split-step Fourier method to detect blow-up, numerical simulations are conducted for several test problems, and the numerical results are compared with the analytical results available in the literature. Good agreement between the numerical and analytical results is observed.Yayın Two-dimensional wave packets in an elastic solid with couple stresses(Pergamon-Elsevier Science Ltd, 2004-08) Babaoğlu, Ceni; Erbay, SaadetThe 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 for the description of elastic waves in the far field. Using a multi-scale expansion of quasi-monochromatic wave solutions, it is shown that the modulation of waves is governed by a system of three non-linear evolution equations. These equations involve amplitudes of a short transverse wave, a long transverse wave and a long longitudinal wave, and will be called the "generalized Davey Stewartson equations". Under some restrictions on parameter values, the generalized Davey-Stewartson equations reduce to the Davey-Stewartson and to the non-linear Schrodinger equations. Finally, some special solutions involving sech-tanh-tanh and tanh-tanh-tanh type solitary wave solutions are presented.Yayın Stability of solitary waves for three-coupled long wave-short wave interaction equations(Oxford Univ Press, 2011-08) Borluk, Handan; Erbay, SaadetIn 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 using variational methods.
