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Explicit series solution of travelling waves with a front of Fisher equation. (English) Zbl 1143.35313
Summary: 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. 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.
MSC:
35C10Series solutions of PDE
35K57Reaction-diffusion equations