Lax Integrability and the Peakon Problem for the Modified Camassa–Holm Equation
Sign Up to like & getrecommendations! Published in 2017 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-017-3076-6
Abstract: Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak… read more here.
Keywords: holm equation; modified camassa; camassa holm;
Stability of peakons for the generalized modified Camassa–Holm equation
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2018.12.014
Abstract: In this paper, we study orbital stability of peakons for the generalized modified Camassa-Holm (gmCH) equation, which is a natural higher-order generalization of the modified Camassa-Holm (mCH) equation, and admits Hamiltonian form and single peakons.… read more here.
Keywords: modified camassa; camassa holm; stability; equation ... See more keywords
Globally conservative solutions for the modified Camassa–Holm (MOCH) equation
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0048245
Abstract: In this paper, we present the globally conservative solutions to the Cauchy problem for the modified Camassa–Holm (MOCH) equation. First, we transform the equation into an equivalent semi-linear system under new variables. Second, according to… read more here.
Keywords: modified camassa; camassa holm; conservative solutions; globally conservative ... See more keywords