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Liouville Integrability of Conservative Peakons for a Modified CH equation
Chang, Xiangke1,2; Szmigielski, Jacek2
AbstractThe modified Camassa-Holm (also called FORQ) equation is one of numerous cousins of the Camassa-Holm equation possessing non-smoth solitons (peakons) as special solutions. The peakon sector of solutions is not uniquely defined: in one peakon sector (dissipative(a)) the Sobolev H-1 norm is not preserved, in the other sector (conservative), introduced in [2], the time evolution of peakons leaves the H-1 norm invariant. In this Letter, it is shown that the conservative peakon equations of the modified Camassa-Holm can be given an appropriate Poisson structure relative to which the equations are Hamiltonian and, in fact, Liouville integrable. The latter is proved directly by exploiting the inverse spectral techniques, especially asymptotic analysis of solutions, developed elsewhere [3].
KeywordConservative peakons Liouville integrability
Funding ProjectNatural Sciences and Engineering Research Council of Canada (NSERC) ; Department of Mathematics and Statistics of the University of Saskatchewan ; PIMS ; Institute of Computational Mathematics, AMSS, CAS ; NSERC[163953]
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000414999400010
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Document Type期刊论文
Corresponding AuthorChang, Xiangke
Affiliation1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, AMSS, POB 2719, Beijing 100190, Peoples R China
2.Univ Saskatchewan, Dept Math & Stat, 106 Wiggins Rd, Saskatoon, SK S7N 5E6, Canada
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GB/T 7714
Chang, Xiangke,Szmigielski, Jacek. Liouville Integrability of Conservative Peakons for a Modified CH equation[J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS,2017,24(4):584-595.
APA Chang, Xiangke,&Szmigielski, Jacek.(2017).Liouville Integrability of Conservative Peakons for a Modified CH equation.JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS,24(4),584-595.
MLA Chang, Xiangke,et al."Liouville Integrability of Conservative Peakons for a Modified CH equation".JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS 24.4(2017):584-595.
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