21 citations · 68 across the 14 of their papers we have counts for
14 papers
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 full dispersion Kadomtsev-Petviashvili equations for dispersive elastic waves
H. A. Erbay, S. Erbay, A. Erkip
Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev-Petviashvili (KP) equation, are interesting from both the physical and mathema…
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…
Numerical Computation of Solitary Wave Solutions of the Rosenau Equation
H. A. Erbay, S. Erbay, A. Erkip
We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the litera…
A semi-discrete numerical method for convolution-type unidirectional wave equations
H. A. Erbay, S. Erbay, A. Erkip
Numerical approximation of a general class of nonlinear unidirectional wave equations with a convolution-type nonlocality in space is considered. A semi-discrete numerical method b…
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…
Convergence of a Semi-Discrete Numerical Method for a Class of Nonlocal Nonlinear Wave Equations
H. A. Erbay, S. Erbay, A. Erkip
In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced th…
Derivation of Generalized Camassa-Holm Equations from Boussinesq-type Equations
H. A. Erbay, S. Erbay, A. Erkip
In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type equation using a two-parameter asymptotic expansion based on two small parameters…
Derivation of the Camassa-Holm equations for elastic waves
H. A. Erbay, S. Erbay, A. Erkip
In this paper we provide a formal derivation of both the Camassa-Holm equation and the fractional Camassa-Holm equation for the propagation of small-but-finite amplitude long waves…
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…