## 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 $$0 < c < +\infty$$ 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:

 35C10 Series solutions to PDEs 35K57 Reaction-diffusion equations

### Keywords:

homotopy analysis method
Full Text:

### References:

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