Stability of the Camassa-Holm solitons

By Adrian Constantin, Walter A. Strauss. Journal of nonlinear science, 2002

393 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/59b13ec1c0b36938c2f85122b0d2299e0da349d7

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Citations in the corpus

Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, background): “The orbital stability of the peaked solitons is proved in [16], and that of the smooth solitons in [18].”
On the Well-Posedness Problem and the Scattering Problem for the Dullin-Gottwald-Holm Equation (2005, methodology): “From (5.2) we infer that solitary waves exist only for c> 2ω and each such speed c determines ϕ uniquely up to translations (see [4, 5, 17 ]).”
Wave Breaking and Global Existence for a Generalized Two-Component Camassa–Holm System (2010, background): “These peakons are shown to be stable [21, 22, 40].”
Blow-up of solutions to the DGH equation (2007, background): “In [2] and [18], it was proved that all solitary waves (peaked when c0 = 0 or smooth when c0 = 0 ) are solitons.”
The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations (2007, background): “The Camassa-Holm equations shares with KdV this integrability property as well as the fact that its solitary waves are solitons [11, 10].”
Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation (2006, background): “The orbital stability of the peaked solitons is proved in [16], and that of the smooth solitons in [ 18 ].”
Traveling wave solutions of the Camassa-Holm equation (2005, background): “1) is an infinitedimensional completely integrable Hamiltonian system: by means of an isospectral problem one can convert the equation into a finite or infinite sequence of linear ordinary differential equations which can be trivially integrated (for the periodic case see [8,20], and for aspects of ”
Inverse scattering transform for the Camassa–Holm equation (2006, background): “Its solitary waves are stable solitons if ω > 0 [2, 15, 17, 26] or peakons if ω = 0 [5, 6].”
Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems (2016, neutral): “properties for CH type and related nonlinear evolution equations, we refer the reader to [12], [13], [11], [15], [16], [6], [23], [49], [53], [50], [17], [45], [8], [42], [43], [44], [4], [3], [64], [18], [5], [47], [48], [10], [9], [70], and the references therein.”
Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition (2007, background): “In the literature [4], cusp soliton was also called breaking wave.”
Stability of multipeakons (2008, neutral): “(3) For κ > 0 it possesses smooth positive solitary waves φκ,c with speed c > 2κ , their orbital stability has been proved in [12] by applying the classical spectral method initiated by Benjamin [2] (see also [21]).”
TOPICAL REVIEW: On the geometric approach to the motion of inertial mechanical systems (2002, background): “The solitons are stable, the appropriate notion of stability being orbital stability [17].”
A Two-component Generalization of the Camassa-Holm Equation and its Solutions (2005, background): “It was also proved in [12,13] that such solitary waves and peakons are stable.”