Explicit series solution of travelling waves with a front of Fisher equation

In this paper, an analytic technique, namely the homotopy analysis method, is employed to solve the Fisher equation, which describes a family of travelling waves with a front. The explicit series solution for all possible wave speeds 0 < c < +∞ is given. Such kind of explicit series solution has never been reported, to the best of author’s knowledge. Our series solution indicates that the solution contains an oscillation part when 0 < c < 2. The proposed analytic approach is general, and can be applied to solve other similar nonlinear travelling wave problems.