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 rate of transformation into such a wave depends on time, and the asymptotics as $$t\to\infty$$ is constructed for it. It is found that the asymptotics cannot be constructed in the form of a power series.