Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study

2020/10/21 by Vartanian, A. · 1 citation
#33E17 #34M35 #34M40 #34M50 #34M55 #34M56 #34M60 #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2010.11235

Abstract

A one-parameter family of trans-series asymptotics of solutions to the Degenerate Painlevé III Equation (DP3E) are parametrised in terms of the monodromy data of an associated two-by-two linear auxiliary problem via the isomonodromy deformation approach: trans-series asymptotics for the associated Hamiltonian and principal auxiliary functions and the solution of one of the sigma-forms of the DP3E are also obtained. The actions of Lie-point symmetries for the DP3E are derived.

Cited by

• Painlevé Property and Generating Functions for Asymptotics

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