On the asymptotics of the traveling wave velocity on a saddle-node trajectory

For a semilinear parabolic partial differential equation, an asymptotic solution is considered that at large times $t$ becomes a wave traveling at a constant speed. The speed of transformation into such a wave depends on time, and an asymptotics is constructed for it as $t\to\infty$. It is found that the asymptotics cannot be constructed in the form of a power series.