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

作　　者：胡伟鹏 邓子辰 韩松梅 范玮 

机构地区：[1]School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University [2]School of Power and Energy, Northwestern Polytechnical University [3]State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian Universityof Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第8期1027-1034,共8页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 10772147 and10632030);the Ph. D. Program Foundation of Ministry of Education of China (No. 20070699028);the Natural Science Foundation of Shaanxi Province of China (No. 2006A07);the Open Foundationof State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802);the Foundation for Fundamental Research of Northwestern Polytechnical University

摘　　要：Nonlinear wave equations have been extensively investigated in the last sev- eral 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 re- sults 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.Nonlinear wave equations have been extensively investigated in the last sev- eral 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 re- sults 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.

关 键 词：MULTI-SYMPLECTIC Landau-Ginzburg-Higgs equation Runge-Kutta method conservation law soliton solution 

分 类 号：O175.2[理学—数学]