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 Chin. Phys. B, 2010, Vol. 19(3): 030401    DOI: 10.1088/1674-1056/19/3/030401
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# Approximate solution for the Klein－Gordon－Schr?dinger equation by the homotopy analysis method

Wang Jia(王佳)a), Li Biao(李彪) a)b)†, and Ye Wang-Chuan(叶望川)a)
a Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China; b MM Key Lab, Chinese Academy of Sciences, Beijing 100080, China
Abstract  The Homotopy analysis method is applied to obtain the approximate solution of the Klein--Gordon--Schr?dinger equation. The Homotopy analysis solutions of the Klein--Gordon--Schr?dinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.
Keywords:  Klein--Gordon--Schr?dinger equation      homotopy analysis method      approximate solution
Received:  03 June 2009      Revised:  24 July 2009      Accepted manuscript online:
 PACS: 05.45.Yv (Solitons) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10735030), National Basic Research Program of China (Grant No.~2007CB814800), Ningbo Natural Science Foundation (Grant No.~2008A610017) and K.C. Wong Magna Fund in Ningbo University.

#### Cite this article:

Wang Jia(王佳), Li Biao(李彪), and Ye Wang-Chuan(叶望川) Approximate solution for the Klein－Gordon－Schr?dinger equation by the homotopy analysis method 2010 Chin. Phys. B 19 030401

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