Hard loss of stability in Painlevé-2 equation

Abstract

A special asymptotic solution of the Painlevé-2 equation with small parameter is studied. This solution has a critical point $t_{\ast }$ corresponding to a bifurcation phenomenon. When $t<t_{\ast }$ the constructed solution varies slowly and when $t>t_{\ast }$ the solution oscillates very fast. We investigate the transitional layer in detail and obtain a smooth asymptotic solution, using a sequence of scaling and matching procedures.

Cited by in corpus (1)

• An asymptotic structure of the bifurcation boundary of the perturbed Painlevé-2 equation