Integral formulas for Painlevé-2 transcendent

2021/03/17 by Kiselev, O. M.
#Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2103.09871

Abstract

In the work we use integral formulas for calculating the monodromy data for the Painlevé-2 equation. The perturbation theory for the auxiliary linear system is constructed and formulas for the variation of the monodromy data are obtained. We also derive a formula for solving the linearized Painlevé-2 equation based on the Fourier-type integral of the squared solutions of the auxiliary linear system of equations.

Related

• The Painlevé transcendents with solvable monodromy
• A unified approach to the Painleve Transcendents
• Painlevé II transcendents and their squares
• Classical transcendental solutions of the Painlevé equations and their degeneration
• Critical behaviours of the fifth Painlevé transcendents and the monodromy data