Inverse Spectral Problem and Peakons of an Integrable Two-component Camassa-Holm System
نویسندگان
چکیده
منابع مشابه
Stability 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 کاملStability 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 کاملPeriodic Conservative Solutions for the Two-component Camassa–holm System
We construct a global continuous semigroup of weak periodic conservative solutions to the two-component Camassa–Holm system, ut − utxx + κux + 3uux − 2uxuxx − uuxxx + ηρρx = 0 and ρt + (uρ)x = 0, for initial data (u, ρ)|t=0 in H1 per ×Lper. It is necessary to augment the system with an associated energy to identify the conservative solution. We study the stability of these periodic solutions by...
متن کاملStability 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...
متن کاملStability of the Camassa-Holm peakons in the dynamics of a shallow-water-type system
The stability of the Camassa-Holm (periodic) peakons in the dynamics of an integrable shallow-water-type system is investigated. A variational approach with the use of the Lyapunov method is presented to prove the variational characterization and the orbital stability of these wave patterns. In addition, a sufficient condition for the global existence of strong solutions is given. Finally, a lo...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2021
ISSN: 1776-0852
DOI: 10.1080/14029251.2018.1452674