Liouville Integrability of Conservative Peakons for a Modified CH equation
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- Conservative peakons, Liouville integrability
The 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 (dissipativea) the Sobolev H1 norm is not preserved, in the other sector (conservative), introduced in , the time evolution of peakons leaves the H1 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 .
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Cite this article
TY - JOUR AU - Xiangke Chang AU - Jacek Szmigielski PY - 2021 DA - 2021/01 TI - Liouville Integrability of Conservative Peakons for a Modified CH equation JO - Journal of Nonlinear Mathematical Physics SP - 584 EP - 595 VL - 24 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1375693 DO - https://doi.org/10.1080/14029251.2017.1375693 ID - Chang2021 ER -