The Painlevé Connection Problem: An Asymptotic Approach. I

DOI10.1002/sapm1992864315zbMath0761.34003OpenAlexW103267628MaRDI QIDQ4022058

Nalini Joshi, Martin D. Kruskal

Publication date: 17 January 1993

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1992864315

zbMATH Keywords

asymptotic behaviorelliptic functionsPainlevé equationsmultiple-scales methodPainlevé connection problem

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items

Connection problem of the first Painlevé transcendents with large initial data, On a general singular solution of the fifth Painlevé equation along the positive real axis, Asymptotic behaviours given by elliptic functions in ${\rm P_I}$ –${\rm P_V}$, Open problems for Painlevé equations, ELLIPTIC ASYMPTOTIC REPRESENTATION OF THE FIFTH PAINLEVÉ TRANSCENDENTS, Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree, Hamiltonian structure of rational isomonodromic deformation systems, Doubly-resonant saddle-nodes in (\protect \mathbb{C}^3,0) and the fixed singularity at infinity in Painlevé equations: analytic classification, Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1, Global asymptotics of the second Painlevé equation in Okamoto's space, A note on an open problem about the first Painlevé equation, Okamoto's space for the first Painlevé equation in Boutroux coordinates, On various approaches to asymptotics of solutions to the third Painlevé equation in a neighborhood of infinity, Existence and uniqueness of Tronquée solutions of the fourth-order Jimbo-Miwa second Painlevé equation, Dynamics of Nonpolar Solutions to the Discrete Painlevé I Equation, Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries

Cites Work

• Monodromy problem and the boundary condition for some Painlevé equations
• Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• Connection formulae for Painlevé functions
• Painlevé functions of the third kind