21 citations · 68 across the 14 of their papers we have counts for
8 papers · 1 filter
Convergence of a linearly regularized nonlinear wave equation to the -system
Hüsnü Ata Erbay, Saadet Erbay, Albert Kohen Erkip
We consider a second-order nonlinear wave equation with a linear convolution term. When the convolution operator is taken as the identity operator, our equation reduces to the clas…
A Comparison of Solutions of Two Convolution-Type Unidirectional Wave Equations
H. A. Erbay, S. Erbay, A. Erkip
In this work, we prove a comparison result for a general class of nonlinear dispersive unidirectional wave equations. The dispersive nature of one-dimensional waves occurs because…
On the convergence of the nonlocal nonlinear model to the classical elasticity equation
H. A. Erbay, S. Erbay, A. Erkip
We consider a general class of convolution-type nonlocal wave equations modeling bidirectional propagation of nonlinear waves in a continuous medium. In the limit of vanishing nonl…
Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations
H. A. Erbay, S. Erbay, A. Erkip
We consider the Cauchy problem defined for a general class of nonlocal wave equations modeling bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose c…
Instability and stability properties of traveling waves for the double dispersion equation
H. A. Erbay, S. Erbay, A. Erkip
In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation $~u_{tt} -u_{xx}+a u_{xxxx}-bu_{xxtt} =…
Existence and Stability of Traveling Waves for a Class of Nonlocal Nonlinear Equations
H. A. Erbay, S. Erbay, A. Erkip
In this article we are concerned with the existence and orbital stability of traveling wave solutions of a general class of nonlocal wave equations: $ u_{tt}-Lu_{xx}=B(\pm |u|^{p-1…
Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations
Saadet Erbay, Husnu A. Erbay, Albert Erkip
In this article we study global existence and blow-up of solutions for a general class of nonlocal nonlinear wave equations with power-type nonlinearities, $u_{tt}-Lu_{xx}=B(- |u|^…
Stability of Solitary Waves for Three Coupled Long Wave - Short Wave Interaction Equations
H. Borluk, S. Erbay
In this paper we consider a three-component system of one dimensional long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We…