Explicit Symplectic Methods for the Nonlinear Schrodinger Equation  

作　　者：Hua Guan Yandong Jiao Ju Liu Yifa Tang 

机构地区：[1]LSEC,ICMSEC,Academy of Mathematics&Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]Department of Scientific Computation and Applied Software,School of Science,Xi’an Jiaotong University,Xi’an 710049,China

出　　处：《Communications in Computational Physics》2009年第8期639-654,共16页计算物理通讯（英文）

基　　金：This research is partially supported by the Informatization Construction of Knowledge Innovation Projects of the Chinese Academy of Sciences“Supercomputing En-vironment Construction and Application”(INF105-SCE);National Natural Science Foundation of China(Grant Nos.10471145 and 10672143).

摘　　要：By performing a particular spatial discretization to the nonlinear Schrodinger equation(NLSE),we obtain a non-integrable Hamiltonian system which can be decomposed into three integrable parts(L-L-N splitting).We integrate each part by calculating its phase flow,and develop explicit symplectic integrators of different orders for the original Hamiltonian by composing the phase flows.A 2nd-order reversible constructed symplectic scheme is employed to simulate solitons motion and invariants behavior of the NLSE.The simulation results are compared with a 3rd-order non-symplectic implicit Runge-Kutta method,and the convergence of the formal energy of this symplectic integrator is also verified.The numerical results indicate that the explicit symplectic scheme obtained via L-L-N splitting is an effective numerical tool for solving the NLSE.

关 键 词：Explicit symplectic method L-L-N splitting nonlinear Schrodinger equation 

分 类 号：O17[理学—数学]