Lax Integrability and the Peakon Problem for the Modified Camassa–Holm Equation
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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;
Changes in the physical structures for new versions of the Degasperis-Procesi-Camassa-Holm model
Sign Up to like & getrecommendations! Published in 2020 at "Chinese Journal of Physics"
DOI: 10.1016/j.cjph.2020.11.010
Abstract: Abstract The goal of this work is to develop new solutions for modified versions of Degasperis-Procesi and Camassa-Holm model (DP-CH). In earlier studies, it has been observed that the new modification caused a deformation in… read more here.
Keywords: holm model; camassa holm; procesi camassa; model ... See more keywords
Geometric approach on the global conservative solutions of the Camassa–Holm equation
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DOI: 10.1016/j.geomphys.2019.04.003
Abstract: Abstract In this paper we construct global weak conservative solutions of the Camassa–Holm (CH) equation on the periodic domain. We first express the equation in Lagrangian flow variable η and then transform it using the… read more here.
Keywords: camassa holm; solutions camassa; holm equation; conservative solutions ... See more keywords
Stability of peakons for the generalized modified Camassa–Holm equation
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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
Non-uniform continuity of the solution map to the rotation-two-component Camassa-Holm system
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DOI: 10.1016/j.jde.2019.10.021
Abstract: Abstract Studied in this paper is the rotation-two-component Camassa-Holm system, which can be considered as a model for the propagation of long-crested shallow-water waves in the equatorial ocean regions with the weak Coriolis effect due… read more here.
Keywords: component camassa; camassa holm; holm system; rotation ... See more keywords
Breaking waves and persistence property for a two-component Camassa–Holm system
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2016.08.035
Abstract: Abstract In this paper, we study a two-component Camassa–Holm system modeling shallow water waves moving over a linear shear flow. Some new blow-up results and a persistence property in weighted L p space are established. read more here.
Keywords: component camassa; camassa holm; holm system; persistence property ... See more keywords
Lipschitz metric for the periodic second-order Camassa–Holm equation
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DOI: 10.1016/j.jmaa.2017.02.018
Abstract: Abstract In this study, we consider the Cauchy problem for the second-order Camassa–Holm equation with periodic initial data u 0 . Using the vanishing viscosity method, the local weak solution of the equation is obtained… read more here.
Keywords: camassa holm; second order; lipschitz metric; holm equation ... See more keywords
Non-uniform continuity on initial data for a Camassa-Holm-type equation in Besov space
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DOI: 10.1016/j.jmaa.2020.124621
Abstract: Abstract In this paper, with special choices of a sequence of low frequency and high frequency initial data g n , f n , based on the established existence estimates, by showing that the difference… read more here.
Keywords: holm type; camassa holm; initial data; non uniform ... See more keywords
Local well-posedness in the critical Besov space and blow-up for an n-component Camassa–Holm system
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DOI: 10.1016/j.jmaa.2021.125423
Abstract: Abstract In this paper, the Cauchy problem of an n-component Camassa–Holm system is considered. The local well-posedness in the critical Besov space ( B 2 , 1 3 2 ) n is established, and it… read more here.
Keywords: camassa holm; system; component camassa; holm system ... See more keywords
Stumpons are non-conservative traveling waves of the Camassa–Holm equation
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DOI: 10.1016/j.physd.2022.133196
Abstract: It is well-known that by requiring solutions of the Camassa–Holm equation to satisfy a particular local conservation law for the energy in the weak sense, one obtains what is known as conservative solutions. As conservative… read more here.
Keywords: stumpons non; traveling waves; camassa holm; holm equation ... See more keywords
A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION
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DOI: 10.1017/fms.2020.22
Abstract: We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving continuity of the… read more here.
Keywords: holm equation; equation; lipschitz metric; camassa holm ... See more keywords