Finite dimensional Hamiltonian system related to Lax pair with symplectic and cyclic symmetries

Details Finite dimensional Hamiltonian system related to Lax pair with symplectic and cyclic symmetries Finite dimensional Hamiltonian system related to Lax pair with symplectic and cyclic symmetries

2011-07-21

arxiv.org/abs/1107.4391v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

For the 1+1 dimensional Lax pair with a symplectic symmetry and cyclic symmetries, it is shown that there is a natural finite dimensional Hamiltonian system related to it by presenting a unified Lax matrix. The Liouville integrability of the derived finite dimensional Hamiltonian systems is proved in a unified way. Any solution of these Hamiltonian systems gives a solution of the original PDE. As an application, the two dimensional hyperbolic $C_n^{(1)}$ Toda equation is considered and the finite dimensional integrable Hamiltonian system related to it is obtained from the general results.

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