High Order Padé Schemes for Nonlinear Wave Propagation Problems

摘要

Split-step Padémethod and split-step fourier method are applied to the higher- order nonlinear Schrdinger equation.It is proved that a combination of Padé scheme and spectral method is the most effective method,which has a spectral-like resolution and good stability nature.In particular,we propose an unconditional stable implicit Padé scheme to solve odd order nonlinear equations.Numerical results demonstrate the excellent performance of Padé schemes for high order nonlinear equations.