Chin. Phys. Lett.  2017, Vol. 34 Issue (9): 090202    DOI: 10.1088/0256-307X/34/9/090202
A Multi-Symplectic Compact Method for the Two-Component Camassa–Holm Equation with Singular Solutions
Xiang Li1, Xu Qian1,2**, Bo-Ya Zhang1, Song-He Song1
1College of Science and State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073
2Academy of Ocean Science and Engineering, National University of Defense Technology, Changsha 410073
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Abstract The two-component Camassa–Holm equation includes many intriguing phenomena. We propose a multi-symplectic compact method to solve the two-component Camassa–Holm equation. Based on its multi-symplectic formulation, the proposed method is derived by the sixth-order compact finite difference method in spatial discretization and the symplectic implicit midpoint scheme in temporal discretization. Numerical experiments finely describe the velocity and density variables in the two-component integrable system and distinctly display the evolvement of the singular solutions. Moreover, the proposed method shows good conservative properties during long-time numerical simulation.
Received: 14 June 2017      Published: 15 August 2017
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  02.70.Bf (Finite-difference methods)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570, the Open Foundation of State Key Laboratory of High Performance Computing of China, the Research Fund of the National University of Defense Technology under Grant No JC15-02-02, and the Fund from HPCL.
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Xiang Li, Xu Qian, Bo-Ya Zhang et al  2017 Chin. Phys. Lett. 34 090202
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Xiang Li
Xu Qian
Bo-Ya Zhang
Song-He Song
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