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Chin. Phys. B, 2013, Vol. 22(3): 030209    DOI: 10.1088/1674-1056/22/3/030209
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Multisymplectic implicit and explicit methods for Klein–Gordon–Schrödinger equations

Cai Jia-Xiang (蔡加祥), Yang Bin (杨斌), Liang Hua (梁华)
School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China
Abstract  We propose multisymplectic implicit and explicit Fourier pseudospectral methods for the Klein–Gordon–Schrödinger equations. We prove that the implicit method satisfies the charge conservation law exactly. Both methods provide accurate solutions in long-time computations and simulate the soliton collision well. Numerical results show the abilities of the two methods in preserving charge, energy, and momentum conservation laws.
Keywords:  Klein–Gordon–Schrödinger equations      multisymplectic method      Fourier pseudospectral method      conservation law  
Received:  12 July 2012      Revised:  05 September 2012      Accepted manuscript online: 
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.70.Bf (Finite-difference methods)  
  45.10.Na (Geometrical and tensorial methods)  
  02.70.Hm (Spectral methods)  
Fund: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11201169) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 10KJB110001).
Corresponding Authors:  Cai Jia-Xiang     E-mail:

Cite this article: 

Cai Jia-Xiang (蔡加祥), Yang Bin (杨斌), Liang Hua (梁华) Multisymplectic implicit and explicit methods for Klein–Gordon–Schrödinger equations 2013 Chin. Phys. B 22 030209

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