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The cauchy problem for a one-dimensional nonlinear elastic peridynamic model
(Elsevier, 2012-04-15)
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-posedness and smoothness of the solutions ...
The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations
(AIMS, 2016-11)
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 belongs are well approximated by the solutions ...
Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity
(Elsevier, 2020-11-15)
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 constitutive relation between the linearized ...
Numerical computation of solitary wave solutions of the Rosenau equation
(Elsevier, 2020-11)
We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave ...
On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations
(American Institute of Mathematical Sciences, 2017-06)
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 equation tend to associated solutions of two ...
A semi-discrete numerical method for convolution-type unidirectional wave equations
(Elsevier, 2021-05-15)
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 based on both a uniform space discretization ...
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 ...
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