Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

doi:10.1088/1674-1056/21/3/030202

中国物理B ›› 2012, Vol. 21 ›› Issue (3): 30202-030202.doi: 10.1088/1674-1056/21/3/030202

张荣培¹,蔚喜军²,冯涛²

收稿日期:2011-06-16 修回日期:2011-09-22 出版日期:2012-02-15 发布日期:2012-02-15
通讯作者: 张荣培,rongpeizhang@163.com E-mail:rongpeizhang@163.com

Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

Zhang Rong-Pei(张荣培)^a)^†, Yu Xi-Jun(蔚喜军)^b), and Feng Tao (冯涛)^b)

a. School of Sciences, Liaoning Shihua University, Fushun 113001, China;
b. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2011-06-16 Revised:2011-09-22 Online:2012-02-15 Published:2012-02-15
Contact: Zhang Rong-Pei,rongpeizhang@163.com E-mail:rongpeizhang@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 11171038).

摘要/Abstract

Abstract: In this work, we present the direct discontinuous Galerkin (DDG) method for the one-dimensional coupled nonlinear Schr?dinger (CNLS) equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.

Key words: direct discontinuous Galerkin method, coupled nonlinear Schr?dinger equation, mass conservation

中图分类号: (Partial differential equations)

02.30.Jr

02.70.Dh (Finite-element and Galerkin methods)

张荣培, 蔚喜军, 冯涛. [J]. 中国物理B, 2012, 21(3): 30202-030202.

Zhang Rong-Pei(张荣培), Yu Xi-Jun(蔚喜军), and Feng Tao (冯涛) . Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method[J]. Chin. Phys. B, 2012, 21(3): 30202-030202.

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Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

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