Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation

ZHANG Yu; DENG Zi-chen; HU Wei-peng

doi:10.3879/j.issn.1000-0887.2013.05.001

Volume 34 Issue 5

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ZHANG Yu, DENG Zi-chen, HU Wei-peng. Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation[J]. Applied Mathematics and Mechanics, 2013, 34(5): 437-444. doi: 10.3879/j.issn.1000-0887.2013.05.001

Citation:

ZHANG Yu, DENG Zi-chen, HU Wei-peng. Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation[J]. Applied Mathematics and Mechanics, 2013, 34(5): 437-444. doi: 10.3879/j.issn.1000-0887.2013.05.001

Citation:

ZHANG Yu, DENG Zi-chen, HU Wei-peng. Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation[J]. Applied Mathematics and Mechanics, 2013, 34(5): 437-444. doi: 10.3879/j.issn.1000-0887.2013.05.001

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Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation

doi: 10.3879/j.issn.1000-0887.2013.05.001

¹School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnincal University, Xi’an 710072, P.R.China;²State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

Received Date: 2013-04-15
Rev Recd Date: 2013-05-03
Publish Date: 2013-05-15

Abstract

Abstract

The nonlinear wave equation, which possesses various forms of analytical solutions, has been investigated widely in last several decades. The multi-symplectic method for the sine-Gordon equation in Hamilton space was proposed. Based on Hamiltonian variational principle, the multi-symplectic formulations of the sine-Gordon equation were deduced, and then, the leap-frog multi-symplectic discretization scheme was constructed using explicit symplectic discrete method. The numerical results for the sine-Gordon equation illustrate that the leap-frog multi-symplectic scheme can simulate the propagation of the soliton and the periodic solution for the sineGordon equation accurately, which show the superiority of the multi-symplectic algorithm when dealing with nonlinear evolution equations.
- structure-preserving,
- multi-symplectic method,
- sine-Gordon equation,
- leap-frog scheme

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References(12)

References

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