Real solutions of the first Painlevé equation with large initial data

Authors

  • Yutian Li School of Science and Engineering, Chinese University of Hong Kong, Shenzhen

Abstract

We consider three special cases of the initial value problem of the first Painlevé (PI) equation. Our approach is based on the method of uniform asymptotics introduced by Bassom, et al. [Arch. Rational Mech. Anal. 143, 241 (1998)]. A rigorous proof of a property of the PI solutions on the negative real axis, recently revealed by Bender and Komijani [J. Phys. A 48, 475202 (2015)], is given by approximating the Stokes multipliers. Moreover, we build a more precise relation between the large initial data of the PI solutions and their three different types of behavior as the independent variable tends to negative infinity. In addition, some limiting form connection formulas are obtained.

Author Biography

  • Yutian Li, School of Science and Engineering, Chinese University of Hong Kong, Shenzhen

    Dr. Yutian Li is now an Assistant Professor at the Chinese University of Hong Kong, Shenzhen. He got his BSc degree in Mathematics at Jilin University, China, and his MPhil and PhD degrees at the City University of Hong Kong. Before joining the Chinese University of Hong Kong, Shenzhen, he worked at the City University as a Postdoctoral Fellow and at the Hong Kong Baptist University as a Research Assistant Professor. His research interests include special functions, asymptotic analysis and partial differential equations. He has published more than 30 journal papers.

SPP 2019 Proceedings cover

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Published

2019-04-06

Issue

2019: Proceedings of the 37th Samahang Pisika ng Pilipinas Physics Conference

Section

Invited Presentations

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How to Cite

[1]
“Real solutions of the first Painlevé equation with large initial data”, Proc. SPP, vol. 37, no. 1, p. SPP-2019-INV-2D-01, Apr. 2019, Accessed: Mar. 27, 2026. [Online]. Available: https://proceedings.spp-online.org/article/view/SPP-2019-INV-2D-01