Peakons, R-Matrix and Toda-Lattice
solv-int
2015-06-26 v1 Exactly Solvable and Integrable Systems
Abstract
The integrability of a family of hamiltonian systems, describing in a particular case the motionof N ``peakons" (special solutions of the so-called Camassa-Holm equation) is established in the framework of the -matrix approach, starting from its Lax representation. In the general case, the -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 -matrix becomes essentially constant, and reduces to the one pertaining to the finite (non-periodic) Toda lattice. Intriguing consequences of such property are discussed and an integrable time discretisation is derived.
Keywords
Cite
@article{arxiv.solv-int/9509012,
title = {Peakons, R-Matrix and Toda-Lattice},
author = {O. Ragnisco and M. Bruschi},
journal= {arXiv preprint arXiv:solv-int/9509012},
year = {2015}
}
Comments
12 plain tex pages