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Volume 6, Issue 3
Explicit Symplectic Methods for the Nonlinear Schrödinger Equation

Hua Guan, Yandong Jiao, Ju Liu & Yifa Tang

Commun. Comput. Phys., 6 (2009), pp. 639-654.

Published online: 2009-06

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  • Abstract

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.

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@Article{CiCP-6-639, author = {}, title = {Explicit Symplectic Methods for the Nonlinear Schrödinger Equation}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {3}, pages = {639--654}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7698.html} }
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 -

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.

Hua Guan, Yandong Jiao, Ju Liu & Yifa Tang. (2020). Explicit Symplectic Methods for the Nonlinear Schrödinger Equation. Communications in Computational Physics. 6 (3). 639-654. doi:
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