TY - JOUR
T1 - Explicit Symplectic Methods for the Nonlinear Schrödinger Equation
JO - Communications in Computational Physics
VL - 3
SP - 639
EP - 654
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7698.html
KW - 
AB - <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>