Integrable symplectic maps via reduction of Backlund transformation

摘要

We discuss the stationary potential equations as illustrative examples to explain how to construct integrable symplectic maps via Backlund transformations. We first give a terse survey of Backlund transformations of the potential KdV equation and the potential fifth-order KdV equation. Then, using Jacobi-Ostrogradsky coordinates, we obtain canonical Hamiltonian forms of the stationary potential equations. Finally, we construct symplectic maps from the reduction of a Backlund transformation and verify that they are integrable.