Patched peakon weak solutions of the modified Camassa–Holm 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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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...
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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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We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassa–Holm equation. Utilizing the solution of the indefinite moment problem given by M. G. Krein and H. Langer, we show that the conservative Camassa–Holm equation is integrable by the inverse spectral transform in the multi-peakon case.
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2019
ISSN: 0167-2789
DOI: 10.1016/j.physd.2018.10.005