Browsing by Subject "Improved Boussinesq equation"
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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 ... -
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 ... -
Convergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equations
(EDP Sciences, 2018-09-13)In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. ... -
Derivation of generalized Camassa-Holm equations from Boussinesq-type equations
(Informa Group, 2016)In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type equation using a two-parameter asymptotic expansion based on two small parameters characterizing nonlinear and dispersive ... -
Derivation of the Camassa-Holm equations for elastic waves
(Elsevier, 2015-06-05)In this paper we provide a formal derivation of both the Camassa–Holm equation and the fractional Camassa–Holm equation for the propagation of small-but-finite amplitude long waves in a nonlocally and nonlinearly elastic ... -
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 ... -
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 ...
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