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Yayın 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) Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, AlbertThis 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 problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in L-2 Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established.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.
