Title: Group classification and some new periodic-like and soliton-like solutions of the generalised Fisher equation with time-variable coefficients

Authors: Mohamed Soror Abdel Latif; Entsar El Shazly; Ahmed Elsaid; Hamed Mohamed Nour

Addresses: Faculty of Engineering, Mathematics and Engineering Physics Department, Mansoura University, P.O. 35516, Mansoura, Egypt ' Faculty of Engineering, Mathematics and Engineering Physics Department, Mansoura University, P.O. 35516, Mansoura, Egypt ' Faculty of Engineering, Mathematics and Engineering Physics Department, Mansoura University, P.O. 35516, Mansoura, Egypt ' Faculty of Engineering, Mathematics and Engineering Physics Department, Mansoura University, P.O. 35516, Mansoura, Egypt

Abstract: In this paper, we perform the group classification of the generalised Fisher equation with time-variable coefficients. Some new periodic-like and soliton-like solutions for some specific forms of the arbitrary functions are obtained. The power series solutions are obtained for some cases when the exact solutions are difficult to be obtained. Also, the convergence of these solutions is investigated.

Keywords: lie symmetries; group classification; generalised Fisher equation.

DOI: 10.1504/IJDSDE.2018.096218

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.4, pp.313 - 325

Received: 25 Apr 2017
Accepted: 20 Oct 2017
Published online: 19 Nov 2018 *

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