The complex multi-symplectic scheme for the generalized sinh-Gordon equation

Weipeng Hu; Zichen Deng; Songmei Han; Wei Fan

doi:10.1007/s11433-009-0190-2

The complex multi-symplectic scheme for the generalized sinh-Gordon equation

Weipeng Hu, Zichen Deng, Songmei Han, Wei Fan

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, the complex multi-symplectic method and the implementation of the generalized sinh- Gordon equation are investigated in detail. The multi-symplectic formulations of the generalized sinh-Gordon equation in Hamiltonian space are presented firstly. The complex method is introduced and a complex semi-implicit scheme with several discrete conservation laws (including a multi-symplectic conservation law (CLS), a local energy conservation law (ECL) as well as a local momentum conservation law (MCL)) is constructed to solve the partial differential equations (PDEs) that are derived from the generalized sinh- Gordon equation numerically. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior and high accuracy.

Original language	English
Pages (from-to)	1618-1623
Number of pages	6
Journal	Science in China, Series G: Physics, Mechanics and Astronomy
Volume	52
Issue number	10
DOIs	https://doi.org/10.1007/s11433-009-0190-2
State	Published - Oct 2009

Keywords

Complex method
Generalized sinh-Gordon equation
Multi-symplectic
Runge-Kutta methods

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10.1007/s11433-009-0190-2

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AU - Deng, Zichen

AU - Han, Songmei

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N2 - In this paper, the complex multi-symplectic method and the implementation of the generalized sinh- Gordon equation are investigated in detail. The multi-symplectic formulations of the generalized sinh-Gordon equation in Hamiltonian space are presented firstly. The complex method is introduced and a complex semi-implicit scheme with several discrete conservation laws (including a multi-symplectic conservation law (CLS), a local energy conservation law (ECL) as well as a local momentum conservation law (MCL)) is constructed to solve the partial differential equations (PDEs) that are derived from the generalized sinh- Gordon equation numerically. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior and high accuracy.

AB - In this paper, the complex multi-symplectic method and the implementation of the generalized sinh- Gordon equation are investigated in detail. The multi-symplectic formulations of the generalized sinh-Gordon equation in Hamiltonian space are presented firstly. The complex method is introduced and a complex semi-implicit scheme with several discrete conservation laws (including a multi-symplectic conservation law (CLS), a local energy conservation law (ECL) as well as a local momentum conservation law (MCL)) is constructed to solve the partial differential equations (PDEs) that are derived from the generalized sinh- Gordon equation numerically. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior and high accuracy.

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KW - Runge-Kutta methods

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The complex multi-symplectic scheme for the generalized sinh-Gordon equation

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Keywords

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