Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints
arXiv:nlin/0103025 · doi:10.1143/JPSJ.70.1241
Abstract
The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems are completely integrable in Liouville sense by finding a full set of integrals of motion and proving their functional independence.
10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001)