Diffusive and inviscid traveling waves of the Fisher equation and nonuniqueness of wave speed

In this paper we present an intuitive explanation for the non-uniqueness of the traveling wave speed in the Fisher equation, showing a similar non-uniqueness property in the case of inviscid traveling waves. More precisely, we prove that traveling waves of the Fisher equation with wave speed c>0c>0 converge to the inviscid traveling wave with speed c>0c>0 as the diffusion vanishes. A complete diagram that shows the relation between the diffusive and inviscid traveling waves is given in this paper.