Degasperis–Procesi peakon dynamical system and finite Toda lattice of CKP type
Degasperis–Procesi peakon dynamical system and finite Toda lattice of CKP type
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DegasperisâProcesi Peakon 动力系统和 CKP 型有限 Toda 晶格
DOI：
10.1088/1361-6544/aad52c
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发表时间：
2018
期刊：
影响因子：
1.7
通讯作者：
Li Shi-Hao
中科院分区：
文献类型：
--
作者：
Chang Xiang-Ke;Hu Xing-Biao;Li Shi-Hao
在本文中，我们提出了一个有限的户田格的CKP型（C-户田）连同一个Lax对。我们的动机是基于Camassa-Holm（CH）峰子动力系统和有限户田晶格在某种意义上可以看作是相反的流动。作为CH方程的一个有趣的类似物，Degasperis-Procesi（DP）方程也支持峰子解的存在。注意到DP方程的峰子解是用与柯西核相关的双矩行列式表示的，我们对这些矩施加了相反的时间演化，并导出了相应的双线性方程。相应的四次表示是一个简化的离散CKP方程的连续极限，因此我们称得到的方程为有限的CKP型户田格。然后，一个非线性版本的C-Toda晶格连同一个Lax对。结果表明，DP峰子晶格和有限C-Toda晶格在一定的变换下形成相反的流动。
In this paper, we propose a finite Toda lattice of CKP type (C-Toda) together with a Lax pair. Our motivation is based on the fact that the Camassa–Holm (CH) peakon dynamical system and the finite Toda lattice may be regarded as opposite flows in some sense. As an intriguing analogue to the CH equation, the Degasperis–Procesi (DP) equation also supports the presence of peakon solutions. Noticing that the peakon solution to the DP equation 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 equation. The corresponding quartic representation is shown to be a continuum limit of a reduced discrete CKP equation, due to which we call the obtained equation a finite Toda lattice of CKP type. Then, a nonlinear version of the C-Toda lattice together with a Lax pair is derived. As a result, it is shown that the DP peakon lattice and the finite C-Toda lattice form opposite flows under a certain transformation.