Simple Method to Generate Integrable Symplectic Maps

摘要

It is shown that by taking stationary flow of integrable evolution equations onlattices, integrable symplectic maps are obtained. An alternative method based on the nonlinearization of a scattering problem is discussed. Its intimate connections with the previous one is explained. Examples of integrable maps are presented. The key points to prove that it is reasonable to expect that stationary flows of integrable discrete evolution equations are integrable discrete time systems, are given.