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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (8): 1027-1034.doi: https://doi.org/10.1007/s10483-009-0809-x

• Articles • 上一篇    下一篇

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

胡伟鹏1,2 邓子辰1,3 韩松梅1 范玮2   

  1. 1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University,Xi’an 710072, P. R. China;
    2. School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, P. R. China;
    3. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian Universityof Technology, Dalian 116023, Liaoning Province, P. R. China
  • 收稿日期:2009-01-12 修回日期:2009-06-20 出版日期:2009-08-01 发布日期:2009-08-01

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

 HU Wei-Peng1,2, DENG Zi-Chen1,3, HAN Song-Mei1, FAN Wei2   

  1. 1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University,Xi’an 710072, P. R. China;
    2. School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, P. R. China;
    3. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian Universityof Technology, Dalian 116023, Liaoning Province, P. R. China
  • Received:2009-01-12 Revised:2009-06-20 Online:2009-08-01 Published:2009-08-01

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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.

关键词: multi-symplectic, Landau-Ginzburg-Higgs equation, Runge-Kutta method, conservation law, soliton solution

Abstract: 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.

Key words: multi-symplectic, Landau-Ginzburg-Higgs equation, Runge-Kutta method, conservation law, soliton solution

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