A New Multi-Symplectic Scheme for the KdV Equation
LV Zhong-Quan1, XUE Mei1, WANG Yu-Shun1,2**
1Jiangsu Key Laboratory for NSLSCS, School of Mathematical Science, Nanjing Normal University, Nanjing 210046 2 Lasg, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
A New Multi-Symplectic Scheme for the KdV Equation
LV Zhong-Quan1, XUE Mei1, WANG Yu-Shun1,2**
1Jiangsu Key Laboratory for NSLSCS, School of Mathematical Science, Nanjing Normal University, Nanjing 210046 2 Lasg, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
摘要We propose a new multi-symplectic integrating scheme for the Korteweg-de Vries (KdV) equation. The new scheme is derived by concatenating spatial discretization of the multi-symplectic Fourier pseudospectral method with temporal discretization of the symplectic Euler scheme. The new scheme is explicit in the sense that it does not need to solve nonlinear algebraic equations. It is verified that the multi-symplectic semi-discretization of the KdV equation under periodic boundary conditions has N semi−discrete multi-symplectic conservation laws. We also prove that the full-discrete scheme has N full-discrete multi-symplectic conservation laws. Numerical experiments of the new scheme on the KdV equation are made to demonstrate the stability and other merits for long-time integration.
Abstract：We propose a new multi-symplectic integrating scheme for the Korteweg-de Vries (KdV) equation. The new scheme is derived by concatenating spatial discretization of the multi-symplectic Fourier pseudospectral method with temporal discretization of the symplectic Euler scheme. The new scheme is explicit in the sense that it does not need to solve nonlinear algebraic equations. It is verified that the multi-symplectic semi-discretization of the KdV equation under periodic boundary conditions has N semi−discrete multi-symplectic conservation laws. We also prove that the full-discrete scheme has N full-discrete multi-symplectic conservation laws. Numerical experiments of the new scheme on the KdV equation are made to demonstrate the stability and other merits for long-time integration.
LV Zhong-Quan;XUE Mei;WANG Yu-Shun;**
. A New Multi-Symplectic Scheme for the KdV Equation[J]. 中国物理快报, 2011, 28(6): 60205-060205.
LV Zhong-Quan, XUE Mei, WANG Yu-Shun, **
. A New Multi-Symplectic Scheme for the KdV Equation. Chin. Phys. Lett., 2011, 28(6): 60205-060205.
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2011, Vol. 28 
