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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 \(0 < c < +\infty \) 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
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