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;
“Local-in-space” Blowup Criterion for a Weakly Dissipative Dullin–Gottwald–Holm Equation
Sign Up to like & getrecommendations! Published in 2020 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-020-01046-y
Abstract: We are concerned with the blowup phenomena of a dissipative Dullin–Gottwald–Holm equation which can describe unidirectional propagation of surface waves in a shallow water regime. A “local-in-space” blowup criterion is obtained by delicate analysis on… read more here.
Keywords: dullin gottwald; dissipative dullin; gottwald holm; holm equation ... 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
Lipschitz metric for the periodic second-order Camassa–Holm equation
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
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
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
Orbital stability of multi-peakons for a generalized Dullin–Gottwald–Holm equation
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DOI: 10.1063/5.0164490
Abstract: In this paper, we consider a generalized Dullin–Gottwald–Holm equation. The equation admits single peakons and multi-peakons. Using energy argument and combining the method of the orbital stability of a single peakon with monotonicity of the… read more here.
Keywords: equation; holm equation; gottwald holm; multi peakons ... See more keywords
Blow-up scenario for a generalized Camassa–Holm equation with both quadratic and cubic nonlinearity
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DOI: 10.1080/00036811.2019.1636970
Abstract: ABSTRACT In this paper, we mainly devote to study an integrable generalized Camassa–Holm equation with both quadratic and cubic nonlinearity proposed by Xia, Qiao and Li [An integrable system with peakon, complex peakon, weak kink,… read more here.
Keywords: equation quadratic; camassa holm; quadratic cubic; blow ... See more keywords
The modified Camassa–Holm equation with self-consistent sources
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DOI: 10.1088/1751-8121/adb549
Abstract: The modified Camassa–Holm equation serves as the dual counterpart to the modified KdV equation. Notably, the modified KdV equation has been shown to possesses the corresponding equation with the self-consistent sources (SCSs). In this paper,… read more here.
Keywords: equation; holm equation; self consistent; modified camassa ... See more keywords
Decay Rate on the Radius of Spatial Analyticity to Solutions for the Modified Camassa–Holm Equation
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DOI: 10.1155/jom/7611055
Abstract: The initial value problem associated with the modified Camassa–Holm equation for initial data u0(x) that is analytic on the line and having uniform radius of spatial analyticity σ0 is considered. We have shown the persistence… read more here.
Keywords: holm equation; radius spatial; modified camassa; camassa holm ... See more keywords
Rare events in the stochastic Camassa-Holm equation
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DOI: 10.21914/anziamj.v58i0.10990
Abstract: We investigate rare or small probability events in the context of large deviations of the stochastic Camassa–Holm equation. By the weak convergence approach and regularization, we get large deviations of the regularized equation. Then, by… read more here.
Keywords: camassa holm; stochastic camassa; holm equation; equation ... See more keywords