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Chin. Phys. B, 2018, Vol. 27(10): 100202    DOI: 10.1088/1674-1056/27/10/100202
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Truncated series solutions to the (2+1)-dimensional perturbed Boussinesq equation by using the approximate symmetry method

Xiao-Yu Jiao(焦小玉)
School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210046, China
Abstract  

In this paper, the (2+1)-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional (2D) similarity reduction equations by using the approximate symmetry method. A step-by-step procedure is used to acquire Jacobi elliptic function solutions to these similarity equations, which generate the truncated series solutions to the original perturbed Boussinesq equation. Aside from some singular area, the series solutions are convergent when the perturbation parameter is diminished.

Keywords:  approximate symmetry method      (2+1)-dimensional perturbed Boussinesq equation      series solutions      convergence of series solutions  
Received:  06 May 2018      Revised:  18 July 2018      Published:  05 October 2018
PACS:  02.20.Hj (Classical groups)  
  02.30.Jr (Partial differential equations)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant No. 11505094) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20150984).

Corresponding Authors:  Xiao-Yu Jiao     E-mail:  jiaoxiaoyu@njue.edu.cn

Cite this article: 

Xiao-Yu Jiao(焦小玉) Truncated series solutions to the (2+1)-dimensional perturbed Boussinesq equation by using the approximate symmetry method 2018 Chin. Phys. B 27 100202

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