Stability of peakons for the generalized Camassa - Holm equation ∗
نویسنده
چکیده
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 our method works.
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.
متن کاملStability of the μ-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.
متن کاملPeakons and periodic cusp wave solutions in a generalized Camassa–Holm equation
By using the bifurcation theory of planar dynamical systems to a generalized Camassa–Holm equation 0960-0 doi:10 * Co E-m mt þ c0ux þ umx þ 2mux 1⁄4 cuxxx with m = u auxx, a 5 0, c0, c are constant, which is called CH-r equation, the existence of peakons and periodic cusp wave solutions is obtained. The analytic expressions of the peakons and periodic cusp wave solutions are given and numerical...
متن کاملStability of multipeakons
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.
متن کاملOrbital Stability of Peakons for a Generalization of the Modified Camassa-holm Equation
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003