Applied Mathematics and Mechanics

, Volume 30, Issue 8, pp 1027–1034 | Cite as

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

  • Wei-peng Hu (胡伟鹏)Email author
  • Zi-chen Deng (邓子辰)
  • Song-mei Han (韩松梅)
  • Wei Fa (范纬)


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 

Chinese Library Classification


2000 Mathematics Subject Classification

35Q05 35J05 35J25 


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Copyright information

© Shanghai University and Springer-Verlag GmbH 2009

Authors and Affiliations

  • Wei-peng Hu (胡伟鹏)
    • 1
    • 2
    Email author
  • Zi-chen Deng (邓子辰)
    • 1
    • 3
  • Song-mei Han (韩松梅)
    • 1
  • Wei Fa (范纬)
    • 2
  1. 1.School of Mechanics, Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’anP. R. China
  2. 2.School of Power and EnergyNorthwestern Polytechnical UniversityXi’anP. R. China
  3. 3.State Key Laboratory of Structural Analysis of Industrial EquipmentDalian University of TechnologyDalianP. R. China

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