Integral formulas for Painlev\'e-2 transcendent
O.M. Kiselev
TL;DR
This paper develops integral formulas to compute monodromy data for the Painlevé-2 equation, introduces perturbation theory for the auxiliary system, and derives solutions for the linearized equation using Fourier-type integrals.
Contribution
It provides new integral formulas and perturbation methods for analyzing the Painlevé-2 equation and its linearization, advancing the analytical tools available for this nonlinear special function.
Findings
Derived formulas for monodromy data variation
Constructed perturbation theory for the auxiliary system
Presented a Fourier-type integral solution for the linearized Painlevé-2
Abstract
In the work we use integral formulas for calculating the monodromy data for the Painlev\'e-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 Painlev\'e-2 equation based on the Fourier-type integral of the squared solutions of the auxiliary linear system of equations.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation