A direct method to find Stokes multipliers in closed form for P$_1$ and more general integrable systems

DOI10.1090/tran/6612zbMath1354.33016arXiv1205.0775OpenAlexW2963770014MaRDI QIDQ2821663

Min Huang, Rodica D. Costin, Ovidiu Costin

Publication date: 22 September 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.0775

zbMATH Keywords

Painlevé equationBorel summabilityStokes multiplierasymptotically conserved quantityPainlevé-Kowalevski propertytritronquées solutiontronquées solution

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Painlevé-type functions (33E17) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Related Items (9)

Rigorous analytical approximation of tritronquée solution to Painlevé-I and the first singularity ⋮ Connection Problem of the First Painlevé Transcendent Between Poles and Negative Infinity ⋮ Asymptotics, ambiguities and resurgence ⋮ Convergence from divergence ⋮ Truncated solutions of Painlevé equation \({\mathrm P}_{\mathrm V}\) ⋮ Representations of hypergeometric functions for arbitrary parameter values and their use ⋮ Tronquée solutions of the Painlevé equation PI ⋮ Resurgent extrapolation: rebuilding a function from asymptotic data. Painlevé I ⋮ Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Poles of tritronquée solution to the Painlevé I equation and cubic anharmonic oscillator
• Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
• Connection formulae for the first Painlevé transcendent in the complex domain
• NIST digital library of mathematical functions
• Painlevé equations -- nonlinear special functions.
• On Borel summation and Stokes phenomena for rank-\(1\) nonlinear systems of ordinary differential equations
• Tronquée solutions of the Painlevé equation PI
• Global Behavior of Solutions of Nonlinear ODEs: First Order Equations
• Poles of intégrale tritronquée and anharmonic oscillators. Asymptotic localization from WKB analysis
• Painlevé functions of the third kind
• Asymptotic Solutions of the Korteweg-deVries Equation
• Second proof of the irreducibility of the first differential equation of painlevé
• Singular normal form for the Painlevé equation P1
• Quasi-linear Stokes phenomenon for the Painlevé first equation
• Symmetrization in the geometric theory of functions of a complex variable
• Solutions of the first and second Painlevé equations are meromorphic
• On the formation of singularities of solutions of nonlinear differential systems in anti-Stokes directions.

This page was built for publication: A direct method to find Stokes multipliers in closed form for P$_1$ and more general integrable systems