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Degasperis-Procesi peakons and finite Toda lattice of CKP type: isospectral deformations of tau-functions related to Cauchy kernel. (arXiv:1712.08306v1 [nlin.SI])
来源于:arXiv
In the literature, it has been revealed that the Camassa-Holm (CH) peakon
dynamical system and the finite Toda lattice may be regarded as opposite flows.
As an intriguing analogue to the CH equation, the Degasperis-Procesi (DP)
equation also supports the presence of peakon solutions. A natural question
arises: does there exist a corresponding lattice of Toda type for the DP peakon
lattice as the CH peakon and Toda lattices do? In this paper, our aim is to
give an answer to this question. Noticing that the tau function of the DP
peakon lattice is expressed in terms of bimoment determinants related to the
Cauchy kernel, we impose opposite time evolution on the moments and derive the
corresponding bilinear equations. By introducing appropriate nonlinear
variables, a novel Toda lattice of CKP type together with a Lax pair is
obtained. As a result, we give a unified picture for the CH peakon and Toda,
Novikov peakon and B-Toda, DP peakon and C-Toda lattices. 查看全文>>