The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs |
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Authors: | Yaming Chen Songhe SongHuajun Zhu |
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Institution: | Department of Mathematics and System Science, Science School, National University of Defense Technology, Changsha, Hunan, 410073, China |
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Abstract: | In this paper, the multi-symplectic Fourier pseudospectral (MSFP) method is generalized to solve two-dimensional Hamiltonian PDEs with periodic boundary conditions. Using the Fourier pseudospectral method in the space of the two-dimensional Hamiltonian PDE (2D-HPDE), the semi-discrete system obtained is proved to have semi-discrete multi-symplectic conservation laws and a global symplecticity conservation law. Then, the implicit midpoint rule is employed for time integration to obtain the MSFP method for the 2D-HPDE. The fully discrete multi-symplectic conservation laws are also obtained. In addition, the proposed method is applied to solve the Zakharov-Kuznetsov (ZK) equation and the Kadomtsev-Petviashvili (KP) equation. Numerical experiments on soliton solutions of the ZK equation and the KP equation show the high accuracy and effectiveness of the proposed method. |
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Keywords: | Multi-symplectic Fourier pseudospectral method Hamiltonian PDE Zakharov-Kuznetsov equation Kadomtsev-Petviashvili equation |
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