26 citations · 107 across the 16 of their papers we have counts for
16 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…
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…
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…