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A New Multi-Symplectic Scheme for the KdV Equation |
| LV Zhong-Quan1, XUE Mei1, WANG Yu-Shun1,2**
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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
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| Cite this article: |
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LV Zhong-Quan, XUE Mei, WANG Yu-Shun 2011 Chin. Phys. Lett. 28 060205 |
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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.
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| Keywords:
02.60.Cb
02.70.Bf
45.10.Na
45.20.Dh
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Received: 22 February 2011
Published: 29 May 2011
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| PACS: |
02.60.Cb
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(Numerical simulation; solution of equations)
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02.70.Bf
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(Finite-difference methods)
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45.10.Na
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(Geometrical and tensorial methods)
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45.20.dh
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(Energy conservation)
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