Asymptotic approach for the rigid condition of appearance of the oscillations in the solution of the Painleve2 equation
Abstract
The asymptotic solution for the Painleve2 equation with small parameter is considered. The solution has algebraic behavior before point $t_*$ and fast oscillating behavior after the point $t_*$. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve1 equation and some elliptic equation with constant coefficients, where the solution of the Painleve1 equation has poles. The uniform smooth asymptotics are constructed in the interval, containing the critical point $t_*$.
 Publication:

arXiv eprints
 Pub Date:
 February 1999
 arXiv:
 arXiv:solvint/9902007
 Bibcode:
 1999solv.int..2007K
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 Latex, 18 pages