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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 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.
