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Multi-symplectic Runge-Kutta methods for Landau-Ginzburg-Higgs equation |
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| Authors: | Wei-peng Hu Zi-chen Deng Song-mei Han Wei Fa |
| Affiliation: | 1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polyteehnical University, Xi'an 710072, P. R. China;School of Power and Energy, Northwestern Polytechnical University, Xi'an 710072, P. R. China 2. School of Mechanics, Civil Engineering and Architecture, Northwestern Polyteehnical University, Xi'an 710072, P. R. China;State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, Liaoning Province,P.R.China 3. School of Mechanics, Civil Engineering and Architecture, Northwestern Polyteehnical University, Xi'an 710072, P. R. China 4. School of Power and Energy, Northwestern Polytechnical University, Xi'an 710072, P. R. China |
| 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 resuits 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. |
| Keywords: | multi-symplectic Landau-Ginzburg-Higgs equation Runge-Kutta method conservation law soliton solution |
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