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Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations
(American Institute of Mathematical Sciences, 2019-05)
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 constitutive equation is given by a convolution ...
Comparison of nonlocal nonlinear wave equations in the long-wave limit
(Taylor & Francis, 2020-11-17)
We consider a general class of convolution-type nonlocal wave equations modeling bidirectional nonlinear wave propagation. The model involves two small positive parameters measuring the relative strengths of the nonlinear ...
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 ...
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