Hard loss of stability in Painlev\'e-2 equation
Mathematical Physics
2015-06-26 v1 math.MP
Abstract
A special asymptotic solution of the Painlev\'e-2 equation with small parameter is studied. This solution has a critical point corresponding to a bifurcation phenomenon. When the constructed solution varies slowly and when 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.
Cite
@article{arxiv.math-ph/0101037,
title = {Hard loss of stability in Painlev\'e-2 equation},
author = {Oleg M. Kiselev},
journal= {arXiv preprint arXiv:math-ph/0101037},
year = {2015}
}