Hard loss of stability in Painlev\'e-2 equation
Abstract
A special asymptotic solution of the Painlev\'e-2 equation with small parameter is studied. This solution has a critical point t* corresponding to a bifurcation phenomenon. When t<t* the constructed solution varies slowly and when t>t* 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.