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Yayın Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity(IOP Publishing, 2010-01) Duruk, Nilay; Erbay, Hüsnü Ata; Erkip, AlbertWe study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for suitable choices of the kernel function. We establish global existence of solutions of the model assuming enough smoothness on the initial data together with some positivity conditions on the nonlinear term. Furthermore, conditions for finite time blow-up are provided.Yayın Interaction of nonlinear waves governed by Boussinesq equation(Elsevier Ltd, 2006-12) Demiray, HilmiIn the present work, the nonlinear interactions of two acoustical waves governed by the Boussinesq equation with different wave numbers, frequencies and the group velocities are examined. For that purpose, we used the reductive perturbation method and obtained the coupled nonlinear Schrodinger equations. The nonlinear plane wave solution to these equations are given for some special cases.
