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Now showing items 11-16 of 16
On the convergence of the nonlocal nonlinear model to the classical elasticity equation
(Elsevier, 2021-12)
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 nonlocality we study the behavior of solutions ...
Instability and stability properties of traveling waves for the double dispersion equation
(Elsevier, 2016-03)
In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation View the MathML source for View the MathML source, View the MathML source. The ...
On the full dispersion Kadomtsev–Petviashvili equations for dispersive elastic waves
(Elsevier, 2022-09)
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 mathematical points of view. This paper studies ...
The Camassa-Holm approximation to the double dispersion equation for arbitrarily long times
(Springer, 2022-09)
In the present paper we prove the validity of the Camassa-Holm equation as a long wave limit to the double dispersion equation which describes the propagation of bidirectional weakly nonlinear and dispersive waves in an ...
A semi-discrete numerical scheme for nonlocally regularized KdV-type equations
(Elsevier, 2022-05)
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 unidirectional wave equations previously studied ...
A comparison of solutions of two convolution-type unidirectional wave equations
(Taylor and Francis, 2023)
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 of a convolution integral in space. For ...
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