Painleve-type asymptotics of an extended modified KdV equation in transition regions

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of an extended modified KdV equation with decaying initial data in two transition regions, completing previous results by Liu et al. in [18]. It turns out that in first region the asymptotics is expressed in terms of second Painleve transcendents, in second region the asymptotics can be given by the sum of the cosine oscillation function and the solution of a Painleve II equation. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The study applies the method of nonlinear steepest descent to analyze the long-time asymptotics of an extended modified KdV equation with decaying initial data in two transition regions, resulting in different asymptotic expressions in each region.