Multi-Symplectic Runge-Kutta Methods for Landau-Ginzburg-Higgs Equation

HU Wei-peng; DENG Zi-chen; HAN Song-mei; FAN Wei

doi:10.3879/j.issn.1000-0887.2009.08.009

Volume 30 Issue 8

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HU Wei-peng, DENG Zi-chen, HAN Song-mei, FAN Wei. Multi-Symplectic Runge-Kutta Methods for Landau-Ginzburg-Higgs Equation[J]. Applied Mathematics and Mechanics, 2009, 30(8): 963-969. doi: 10.3879/j.issn.1000-0887.2009.08.009

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Multi-Symplectic Runge-Kutta Methods for Landau-Ginzburg-Higgs Equation

doi: 10.3879/j.issn.1000-0887.2009.08.009

1.
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnincal University, Xi'an 710072, P. R. China;

Received Date: 2009-01-12
Rev Recd Date: 2009-06-20
Publish Date: 2009-08-15

Abstract

Abstract

The nonlinear wave equation, describing many important physical phenomena, has been investigated widely in last several decades. Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, was sdudied based on the multisymplectic theory in Hamilton space. The multi symplectic Runge-Kutta method was reviewed and a semiimplicit scheme with certain discrete conservation laws was constructed to solve the first order partial differential equations that were derived from the LandauGinzburg-Higgs equation. The results of numerical experiment for soliton solution of the Landau-Ginzburg-Higgs equation were reported finally, which show that the multi symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.
- multi- symplectic,
- Landau-Ginzburg-Higgs equation,
- Runge-Kutta method,
- conservation law,
- soliton solution

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References(9)

References

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