Browsing Natural and Mathematical Sciences by Subject "Improved Boussinesq equation"
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The CamassaHolm equation as the longwave limit of the improved Boussinesq equation and of a class of nonlocal wave equations
(AIMS, 201611)In the present study we prove rigorously that in the longwave 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 longwave limit
(Taylor & Francis, 20201117)We consider a general class of convolutiontype 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 semidiscrete numerical method for a class of nonlocal nonlinear wave equations
(EDP Sciences, 20180913)In this article, we prove the convergence of a semidiscrete 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 the CamassaHolm equations for elastic waves
(Elsevier, 20150605)In this paper we provide a formal derivation of both the Camassa–Holm equation and the fractional Camassa–Holm equation for the propagation of smallbutfinite amplitude long waves in a nonlocally and nonlinearly elastic ... 
Longtime existence of solutions to nonlocal nonlinear bidirectional wave equations
(American Institute of Mathematical Sciences, 201905)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 ...
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