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arXiv · 2005.03440

On the connection problem for the second Painlevé equation with large initial data

Wen-Gao Long·Zhao-Yun Zeng
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Abstract

We consider two special cases of the connection problem for the second Painlevé 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.

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Wen-Gao Long, Zhao-Yun Zeng. 2021-03-11. On the connection problem for the second Painlevé equation with large initial data. https://arxiv.org/abs/2005.03440

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