Peakon solutions of the shallow water equation
نویسندگان
چکیده
منابع مشابه
A New Integrable Equation with Peakon Solutions
We consider a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, which was recently obtained by Degasperis and Procesi using the method of asymptotic integrability. We prove the exact integrability of the new equation by constructing its Lax pair, and we explain its connection with a negative flow in the Kaup-Kupershmidt hierarchy via a recipro...
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Submitted: Nov 12, 2013; Accepted: Dec 18, 2013; Published: Dec 22, 2013 Abstract: In this article, we have employed an enhanced (G′/G)-expansion method to find the exact solutions first and then the solitary wave solutions of the nonlinear generalized shallow water wave equation. Here we have derived solitons, singular solitons and periodic wave solutions through the enhanced (G′/G)-expansion ...
متن کاملMulti-peakon solutions of the Degasperis–Procesi equation
We present an inverse scattering approach for computing n-peakon solutions of the Degasperis–Procesi equation (a modification of the Camassa– Holm (CH) shallow water equation). The associated non-self-adjoint spectral problem is shown to be amenable to analysis using the isospectral deformations induced from the n-peakon solution, and the inverse problem is solved by a method generalizing the c...
متن کاملElastic collisions among peakon solutions for the Camassa–Holm equation
The purpose of this paper is to study the dynamics of the interaction among a special class of solutions of the one-dimensional Camassa-Holm equation. The equation yields soliton solutions whose identity is preserved through nonlinear interactions. These solutions are characterized by a discontinuity at the peak in the wave shape and are thus called peakon solutions. We apply a particle method ...
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In this paper, the peakons of a generalized CH-KP equation are studied by using bifurcation and simulation methods. The representations of peakons are given, and their planar graphs are showed. These results are supplement to investigate CH-KP equation.
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2001
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00118-x