Volume 7, Issue 3
Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrödinger Equation with Trapped Term

Jialin Hong & Linghua Kong

Commun. Comput. Phys., 7 (2010), pp. 613-630.

Published online: 2010-07

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  • Abstract

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplectic Fourier spectral (MSFS) methods will be employed to solve the fourth-order Schrödinger equations with trapped term. Using the idea of split-step numerical method and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventional multi-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.

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@Article{CiCP-7-613, author = {}, title = {Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrödinger Equation with Trapped Term}, journal = {Communications in Computational Physics}, year = {2010}, volume = {7}, number = {3}, pages = {613--630}, abstract = {

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplectic Fourier spectral (MSFS) methods will be employed to solve the fourth-order Schrödinger equations with trapped term. Using the idea of split-step numerical method and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventional multi-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2009.09.057}, url = {http://global-sci.org/intro/article_detail/cicp/7646.html} }
TY - JOUR T1 - Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrödinger Equation with Trapped Term JO - Communications in Computational Physics VL - 3 SP - 613 EP - 630 PY - 2010 DA - 2010/07 SN - 7 DO - http://dor.org/10.4208/cicp.2009.09.057 UR - https://global-sci.org/intro/article_detail/cicp/7646.html KW - AB -

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplectic Fourier spectral (MSFS) methods will be employed to solve the fourth-order Schrödinger equations with trapped term. Using the idea of split-step numerical method and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventional multi-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.

Jialin Hong & Linghua Kong. (2020). Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrödinger Equation with Trapped Term. Communications in Computational Physics. 7 (3). 613-630. doi:10.4208/cicp.2009.09.057
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