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math.AP2017
On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations
H. A. Erbay, S. Erbay, A. Erkip
We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq eq…
math.AP2016★ 1 cited
The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations
H. A. Erbay, S. Erbay, A. Erkip
In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation b…
math.AP2010★ 13 cited
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
H. A. Erbay, S. Erbay, A. Erkip
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 nonloc…