Numerical Methods For Singular Perturbation Problem Of Nonlinear Schro(?)dinger-wave Equation

Nonlinear Schr(o|¨)dinger-wave equation with perturbation is a kind of typical equa-tions in Plasma physics. Because of the singular phenomenon, the research of nu-merical methods of the NLSW equation with perturbation is always under the spot-light. This paper will research the exact solution and numerical method about theNLSW equation with perturbation. Firstly, we present 1-d and 2-d solitary wave so-lutions for NLSW equation. Furthermore, we derive the 1-d solitary wave solutionfor NLSW equation with perturbation. Secondly, we introduce the Multi-symplecticFourier pseudospectral method for 2-d NLSW equation and derive several conserva-tion quantities in 2-d Hamilton system. Thirdly, we introduce the wave-integrator fac-tor Fourier pseudospectral method for 1-d NLSW equation, which is a very e?cientnumerical method for solving singular perturbation problem. In the end, we presentsome results of numerical experiments.