Approximate solution for the Klein－Gordon－Schr?dinger equation by the homotopy analysis method

doi:10.1088/1674-1056/19/3/030401

中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30401-030401.doi: 10.1088/1674-1056/19/3/030401

Approximate solution for the Klein－Gordon－Schr?dinger equation by the homotopy analysis method

王佳¹, 叶望川¹, 李彪²

(1)Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China; (2)Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China;MM Key Lab, Chinese Academy of Sciences, Beijing 100080, China

收稿日期:2009-06-03 修回日期:2009-07-24 出版日期:2010-03-15 发布日期:2010-03-15
基金资助:
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.

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

Received:2009-06-03 Revised:2009-07-24 Online:2010-03-15 Published:2010-03-15
Supported by:
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.

摘要/Abstract

摘要： 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.

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.

Key words: Klein--Gordon--Schr?dinger equation, homotopy analysis method, approximate solution

中图分类号: (Solitons)

05.45.Yv

02.60.Lj (Ordinary and partial differential equations; boundary value problems)

王佳, 李彪, 叶望川. Approximate solution for the Klein－Gordon－Schr?dinger equation by the homotopy analysis method[J]. 中国物理B, 2010, 19(3): 30401-030401.

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[J]. Chin. Phys. B, 2010, 19(3): 30401-030401.

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Approximate solution for the Klein－Gordon－Schr?dinger equation by the homotopy analysis method

Approximate solution for the Klein－Gordon－Schr?dinger equation by the homotopy analysis method

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