Finite-dimensional integrable systems associated with Davey-Stewartson I equation
Exactly Solvable and Integrable Systems
2009-11-07 v1
Abstract
For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems with a constraint of Neumann type. The full set of involutive conserved integrals is obtained and their functional independence is proved. Therefore, the Hamiltonian systems are completely integrable in Liouville sense. A periodic solution of the Davey-Stewartson I equation is obtained by solving these classical Hamiltonian systems as an example.
Cite
@article{arxiv.nlin/0103045,
title = {Finite-dimensional integrable systems associated with Davey-Stewartson I equation},
author = {Zixiang Zhou and Wen-Xiu Ma and Ruguang Zhou},
journal= {arXiv preprint arXiv:nlin/0103045},
year = {2009}
}
Comments
18 pages, LaTeX