Work

On the asymptotics of real solutions for the Painlevé I equation

Year: 2024

Type: article

Abstract: In this paper, we revisit the asymptotic formulas of real Painlevé I transcendents as the independent variable tends to negative infinity, which were initially derived by Kapaev with the complex WKB method. Using the Riemann–Hilbert method, we improve the error estimates of the oscillatory type asymptotics and provide precise error estimates of the singular type asymptotics. We also establish the corresponding asymptotics for the associated Hamiltonians of real Painlevé I transcendents. In addition, two typos in the mentioned asymptotic formulas in literature are corrected.

Source: Analysis and Applications

DOI: 10.1142/s0219530524500441

Authors: Wen-Gao Long, Jun Xia

Institutions: Hunan University of Science and Technology, Guangdong Polytechnic Normal University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Hunan Province, Basic and Applied Basic Research Foundation of Guangdong Province

Awards: G1244771654, G4224015930, G5969001893, G6101512643