Multi-symplectic Runge-Kutta methods for Landau-Ginzburg-Higgs equation

被引：0
|
作者：
Wei-peng Hu
Zi-chen Deng
Song-mei Han
Wei Fa
机构：
[1] Northwestern Polytechnical University,School of Mechanics, Civil Engineering and Architecture
[2] Northwestern Polytechnical University,School of Power and Energy
[3] Dalian University of Technology,State Key Laboratory of Structural Analysis of Industrial Equipment
来源：
Applied Mathematics and Mechanics | 2009年 / 30卷
关键词：
multi-symplectic; Landau-Ginzburg-Higgs equation; Runge-Kutta method; conservation law; soliton solution; O175.24; 35Q05; 35J05; 35J25;
D O I：
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学科分类号：
摘要：
Nonlinear wave equations have been extensively investigated in the last several decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations (PDEs) derived from the Landau-Ginzburg-Higgs equation. The numerical results for the soliton solution of the Landau-Ginzburg-Higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.
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页码：1027 / 1034
页数：7
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