A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions
Ming Chen,Si-Qi Liu,Youjin Zhang +2 more
Reads0
Chats0
TLDR
An explicit reciprocal transformation between a 2-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established in this paper.Abstract:
An explicit reciprocal transformation between a 2-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established, this transformation enables one to obtain solutions of the 2-CH system from those of the first negative flow of the AKNS hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH system are presented.read more
Citations
More filters
Journal ArticleDOI
On an integrable two-component Camassa–Holm shallow water system
TL;DR: In this paper, a two-component integrable system of coupled equations was derived in the context of shallow water theory and it was shown that while small initial data develop into global solutions, for some initial data wave breaking occurs.
Journal ArticleDOI
On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
Guilong Gui,Guilong Gui,Yue Liu +2 more
TL;DR: In this paper, a two-component Camassa-Holm system is considered, and a wave-breaking criterion for strong solutions is determined in the lowest Sobolev space Hs, s>32 by using the localization analysis in the transport equation theory.
Journal ArticleDOI
Global existence and blow-up phenomena for an integrable two-component Camassa–Holm shallow water system
Chunxia Guan,Zhaoyang Yin +1 more
TL;DR: In this article, a new global existence result and several new blow-up results of strong solutions to the system were presented, and the results for the system are sharp and improve considerably earlier results.
Journal ArticleDOI
On a Camassa-Holm type equation with two dependent variables
TL;DR: In this article, a generalization of the Camassa-Holm (CH) equation with two dependent variables, called CH2, was considered, and an alternative derivation of it based on the theory of Hamiltonian structures on (the dual of) a Lie algebra was provided.
Journal ArticleDOI
On the Cauchy problem for the two-component Camassa–Holm system
Guilong Gui,Guilong Gui,Yue Liu +2 more
TL;DR: In this article, the authors established the local well-posedness of the two-component Camassa-Holm system in a range of the Besov spaces and derived a wave-breaking mechanism for strong solutions.
References
More filters
Journal ArticleDOI
An integrable shallow water equation with peaked solitons
Roberto Camassa,Darryl D. Holm +1 more
TL;DR: A new completely integrable dispersive shallow water equation that is bi-Hamiltonian and thus possesses an infinite number of conservation laws in involution is derived.
Journal ArticleDOI
The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
Journal ArticleDOI
Symplectic structures, their Bäcklund transformations and hereditary symmetries
TL;DR: In this paper, it was shown that compatible symplectic structures lead in a natural way to hereditary symmetries, and that a hereditary symmetry is an operator-valued function which immediately yields a hierarchy of evolution equations, each having infinitely many commuting symmetry all generated by this hereditary symmetry.
Book ChapterDOI
A New Integrable Shallow Water Equation
TL;DR: In this article, a new integrable dispersive dispersive shallow water equation for unidirectional wave motion is presented, which is obtained by using a small-wave-amplitude asymptotic expansion directly in the Hamiltonian for the vertically averaged incompressible Euler's equations, after substituting a solution ansatz of columnar fluid motion.
Journal ArticleDOI
On the scattering problem for the camassa-Holm equation
TL;DR: The Camassa-Holm equation as mentioned in this paper has a number of constants of motion arising as eigenvalues of an associated spectral problem, and the spectral picture is described and discussed in detail.
Related Papers (5)
Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support.
Peter J. Olver,Philip Rosenau +1 more
Wave breaking for nonlinear nonlocal shallow water equations
Adrian Constantin,Joachim Escher +1 more