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;
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
Globally conservative solutions for the modified Camassa–Holm (MOCH) equation
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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
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