Stability of the μ-Camassa-Holm Peakons
نویسندگان
چکیده
The μ-Camassa–Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa–Holm equation. We prove that the periodic peaked traveling wave solutions (peakons) of the μCH equation are orbitally stable.
منابع مشابه
Stability of the mu-Camassa- Holm Peakons
The μ-Camassa-Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa-Holm equation. We prove that the periodic peaked traveling wave solutions (peakons) of the μCH equation are orbitally stable. AMS SUBJECT CLASSIFICATION (2000): 35Q35, 37K45.
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The Camassa-Holm equation possesses well-known peaked solitary waves that are called peakons. Their orbital stability has been established by Constantin and Strauss in [6]. We prove here the stability of ordered trains of peakons. We also establish a result on the stability of multipeakons.
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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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ورودعنوان ژورنال:
- J. Nonlinear Science
دوره 23 شماره
صفحات -
تاریخ انتشار 2013