34 citations · 198 across the 24 of their papers we have counts for
24 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…
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 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…
Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity
Husnu A. Erbay, Albert Erkip, Yasemin Sengul
In this work we prove local existence of strong solutions to the initial-value problem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear con…
A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity
Husnu A. Erbay, Yasemin Sengul
We introduce a one-dimensional stress-rate type nonlinear viscoelastic model for solids that obey the assumptions of the strain-limiting theory. Unlike the classical viscoelasticit…
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…
Comparison of nonlocal nonlinear wave equations in the long-wave limit
H. A. Erbay, S. Erbay, A. Erkip
We consider a general class of convolution-type nonlocal wave equations modeling bidirectional nonlinear wave propagation. The model involves two small positive parameters measurin…
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…
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…
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…
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…
Traveling waves in one-dimensional nonlinear models of strain-limiting viscoelasticity
H. A. Erbay, Y. Şengül
In this article we investigate traveling wave solutions of a nonlinear differential equation describing the behaviour of one-dimensional viscoelastic medium with implicit constitut…
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|^…
Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations
Ceni Babaoglu, Husnu A. Erbay, Albert Erkip
This study deals with the analysis of the Cauchy problem of a general class of nonlocal nonlinear equations modeling the bi-directional propagation of dispersive waves in various c…
The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model
H. A. Erbay, A. Erkip, G. M. Muslu
This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-…
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…