@Article{CiCP-6-639,
author = {Hua Guan, Yandong Jiao, Ju Liu and Yifa Tang},
title = {Explicit Symplectic Methods for the Nonlinear Schrödinger Equation},
journal = {Communications in Computational Physics},
year = {2009},
volume = {6},
number = {3},
pages = {639--654},
abstract = {<p style="text-align: justify;">By performing a particular spatial discretization to the nonlinear
Schrödinger 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7698.html}
}