Abstract
For the Fisher-type wave equation, which has two stable states and one unstable state, it is proved that only in two particular cases, the corresponding travelling wave equation admits a double parameter Lie group, and based on a method different to the traditional one, its two independent first integrals are given. It is proved further that in the two integrable cases, the different bounded and non-trivial travelling wave solutions, which are corresponding the invariant manifolds of the corresponding equation under the Lie transformation, can be expressed with elementary functions although they cannot be obtained directly from the two independent first integrals.
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