Asymptotics of the solution output to a traveling wave in the KPP equation

For a semilinear parabolic partial differential equation, an asymptotic solution is considered, which at long times $t$ goes to a traveling wave. The speed of such a wave depends on time and an asymptotic is constructed for it at $t\to\infty$. It was found out that the asymptotics contains logarithms and cannot be constructed as a power series.