Orbital Stability of Peakons and Multi-peakons for a Generalized Cubic–Quintic Camassa–Holm Type Equation
نویسندگان
چکیده
Abstract The peakons and mulit-peakons for a generalized cubic–quintic Camassa–Holm type equation have been obtained by Weng et al. (Monatsh Math, 2022. https://doi.org/10.1007/s00605-022-01699-w ). In this paper, constructing certain Lyapunov functionals, we prove that the were orbitally stable in energy space. Furthermore, using argument combining method of orbital stability with monotonicity local norm, also sum N sufficiently decoupled is
منابع مشابه
Stability of peakons for the generalized Camassa - Holm equation ∗
We study the existence of minimizers for a constrained variational problems in H(R). These minimizers are stable waves solutions for the Generalized Camassa-Holm equation, and their derivative may have a singularity (in which case the travelling wave is called a peakon). The existence result is based on a method developed by the same author in a previous work. By giving examples, we show how ou...
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Abstract. The Camassa-Holm equation possesses well-known peaked solitary waves that can travel to both directions. The positive ones travel to the right and are called peakon whereas the negative ones travel to the left and are called antipeakons. Their orbital stability has been established by Constantin and Strauss in [20]. In [28] we have proven the stability of trains of peakons. Here, we c...
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The orbital stability of the peaked solitary-wave solutions for a generalization of the modified Camassa-Holm equation with both cubic and quadratic nonlinearities is investigated. The equation is a model of asymptotic shallow-water wave approximations to the incompressible Euler equations. It is also formally integrable in the sense of the existence of a Lax formulation and bi-Hamiltonian stru...
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The Degasperis-Procesi equation can be derived as a member of a oneparameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the CamassaHolm equation. It is noted that the Degasperis-Procesi equation, unlike the Camassa-Holm equation, has not only peakon solitons but also shock peakons. In this paper, we study the orbital sta...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2022
ISSN: ['1776-0852', '1402-9251']
DOI: https://doi.org/10.1007/s44198-022-00093-2