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

摘要

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.