26 citations · 40 across the 5 of their papers we have counts for
5 papers
A semi-discrete numerical scheme for nonlocally regularized KdV-type equations
H. A. Erbay, S. Erbay, A. Erkip
A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The class differs from the class of the nonlinear nonlocal unidir…
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…
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…
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…
Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations
N. Duruk, H. A. Erbay, A. Erkip
We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier…