Global weak solutions for a new periodic integrable equation with peakon solutions
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...
متن کاملGlobal Weak Solutions for a Shallow Water Equation
where α, γ, ω are given real constants. Equation (1) was first introduced as a model describing propagation of unidirectional gravitational waves in a shallow water approximation over a flat bottom, with u representing the fluid velocity [DGH01]. For α = 0 and for α = 1, γ = 0 we obtain the Korteweg–de Vries and the Camassa–Holm [CH93, J02] equations, respectively. Both of them describe unidire...
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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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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: Journal of Functional Analysis
سال: 2004
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2003.07.010