Finite-dimensional integrable systems associated with Davey-Stewartson I equation

Details Finite-dimensional integrable systems associated with Davey-Stewartson I equation Finite-dimensional integrable systems associated with Davey-Stewartson I equation

2001-03-24

arxiv.org/abs/nlin/0103045v1

Nonlinearity 14 (2001), 701-717

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, LaTeX

Scientific paper

10.1088/0951-7715/14/4/303

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.

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