Peakons, r-matrix and Toda lattice

O. Ragnisco and M. Bruschi

Physica A: Statistical Mechanics and its Applications, 1996, vol. 228, issue 1, 150-159

Abstract: The integrability of a family of Hamiltonian systems, describing in a particular case the motion of N “peakons” (special solutions of the so-called Camassa—Holm equation) is established in the framework of the r-matrix approach, starting from its Lax representation. In the general case, the r-matrix is a dynamical one and has an interesting though complicated structure. However, for a particular choice of the relevant parameters in the Hamiltonian (the one corresponding to the pure “peakons” case), the r-matrix becomes essentially constant, and reduces to the one pertaining to the finite (non-periodic) Toda lattice. Intriguing consequences of this property are discussed and an integrable time discretisation is derived.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:228:y:1996:i:1:p:150-159

DOI: 10.1016/0378-4371(95)00438-6

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