@Article{AAMM-10-1069,
author = {Mu , ZhenguoLi , HaochenWang , Yushun and Cai , Wenjun},
title = {A Galerkin Splitting Symplectic Method for the Two Dimensional Nonlinear Schrödinger Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {5},
pages = {1069--1089},
abstract = {<p style="text-align: justify;">In this paper, we propose a Galerkin splitting symplectic (GSS) method for
solving the 2D nonlinear Schrödinger equation based on the weak formulation of the equation. First, the model equation is discretized by the Galerkin method in spatial
direction by a selected finite element method and the semi-discrete system is rewritten
as a finite-dimensional canonical Hamiltonian system. Then the resulted Hamiltonian
system is split into a linear Hamiltonian subsystem and a nonlinear subsystem. The
linear Hamiltonian subsystem is solved by the implicit midpoint method and the nonlinear
subsystem is integrated exactly. By the Strang splitting method, we obtain a
fully implicit scheme for the 2D nonlinear Schrödinger equation (NLS), which is symmetric and of order 2 in time. Furthermore, we apply the FFT technique to improve
computation efficiency of the new scheme. It is proven that our scheme preserves the
mass conservation and the symplectic conservation. Comprehensive numerical experiments
are carried out to illustrate the accuracy of the scheme as well as its conservative
properties.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2017-0222},
url = {http://global-sci.org/intro/article_detail/aamm/12589.html}
}