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A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity
(Springer Nature, 2020-05-28)
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 viscoelasticity theory, the critical hypothesis in the ...
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 ...
Transverse linear instability of solitary waves for coupled long-wave-short-wave interaction equations
(Elsevier, 2012-12)
In this paper, we investigate the transverse linear instability of one-dimensional solitary wave solutions of the coupled system of two-dimensional long-wave–short-wave interaction equations. We show that the one-dimensional ...
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 ...
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 ...
Convergence of a linearly regularized nonlinear wave equation to the p-system
(TÜBİTAK, 2023)
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 classical elasticity equation which can be ...
Dispersive transverse waves for a strain-limiting continuum model
(Sage, 2023-10)
It is well known that propagation of waves in homogeneous linearized elastic materials of infinite extent is not dispersive. Motivated by the work of Rubin, Rosenau, and Gottlieb, we develop a generalized continuum model ...
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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