On the connection problem for the second Painlev\'e equation with large initial data
Classical Analysis and ODEs
2021-03-12 v2 Mathematical Physics
math.MP
Abstract
We consider two special cases of the connection problem for the second Painlev\'e equation (PII) using the method of uniform asymptotics proposed by Bassom et al.. We give a classification of the real solutions of PII on the negative (positive) real axis with respect to their initial data. By product, a rigorous proof of a property associate with the nonlinear eigenvalue problem of PII on the real axis, recently revealed by Bender and Komijani, is given by deriving the asymptotic behavior of the Stokes multipliers.
Keywords
Cite
@article{arxiv.2005.03440,
title = {On the connection problem for the second Painlev\'e equation with large initial data},
author = {Wen-Gao Long and Zhao-Yun Zeng},
journal= {arXiv preprint arXiv:2005.03440},
year = {2021}
}
Comments
25 pages,4 figures. arXiv admin note: text overlap with arXiv:1612.01350