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Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle
Yi Wei1, Xing-Qiu Zhang2, Zhu-Yan Shao2
1School of Medical Information Engineering, Jining Medical University, Rizhao, 276826, Shandong, P.R. China. weiyiwy@126.com.
Abstract:
The variational principle is used to construct a multi-symplectic structure of the generalized KdV-type equation. Accordingly, the local energy conservation law, the local momentum conservation law, and the Cartan form of the generalized KdV-type equation are given. An explicit multi-symplectic scheme for the generalized KdV equation based on the Fourier pseudo-spectral method and the symplectic Euler scheme is constructed. Through a numerical examination, the explicit multi-symplectic Fourier pseudo-spectral scheme for the generalized KdV equation not only preserve the discrete global energy conservation law and the global momentum conservation law with high accuracy, but show long-time numerical stability as well.
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