A refined asymptotic behavior of traveling wave solutions for degenerate nonlinear parabolic equations

In this paper, we consider the asymptotic behavior of traveling wave solutions of the degenerate nonlinear parabolic equation: $u_{t}=u^{p}(u_{xx}+u)-δu$ ($δ= 0$ or $1$) for $ξ\equiv x - ct \to - \infty$ with $c>0$. We give a refined one of them, which was not obtain in the preceding work [Ichida-Sakamoto, 2020], by an appropriate asymptotic study and properties of the Lambert $W$ function.

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