WKB analysis of Painlevé transcendents with a large parameter. III: Local reduction of 2-parameter Painlevé transcendents
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Publication:1385242
DOI10.1006/aima.1997.1716zbMath0901.34057OpenAlexW201178184MaRDI QIDQ1385242
Takahiro Kawai, Yoshitsugu Takei
Publication date: 26 November 1998
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/aima.1997.1716
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20)
Related Items (15)
EXACT SOLUTIONS FOR THE SINGULARLY PERTURBED RICCATI EQUATION AND EXACT WKB ANALYSIS ⋮ 2-parameter \(\tau\)-function for the first Painlevé equation: topological recursion and direct monodromy problem via exact WKB analysis ⋮ Voros coefficients for the hypergeometric differential equations and Eynard-Orantin's topological recursion. I: For the Weber equation ⋮ Riccati equations revisited: linearization and analytic interpretation of instanton-type solutions ⋮ On the Stokes geometry of a unified family of \(P_{\mathrm{J}}\)-hierarchies (J=I, II, IV, 34) ⋮ Exact WKB analysis for the degenerate third Painlevé equation of type \((D_8)\) ⋮ Singular-perturbative reduction to Birkhoff normal form and instanton-type formal solutions of Hamiltonian systems ⋮ Instanton-type solutions for the second and the fourth Painlevé hierarchies with a large parameter ⋮ On the singularity structure of WKB solution of the boosted Whittaker equation: its relevance to resurgent functions with essential singularities ⋮ On Stokes Phenomena for the Alternate Discrete PI Equation ⋮ WKB analysis of higher order Painlevé equations with a large parameter. II. Structure theorem for instanton-type solutions of \((P_J)_m (J= I, 34\), II-2 or IV) near a simple \(P\)-turning point of the first kind ⋮ Reconstructing GKZ via topological recursion ⋮ WKB analysis of higher order Painlevé equations with a large parameter -- local reduction of 0-parameter solutions for Painlevé hierarchies \((P_{J})\) (\(J=\text{ I, II-1 or II-2}\)) ⋮ On an exact WKB approach to Ablowitz-Segur's connection problem for the second Painlevé equation ⋮ Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries
Cites Work
- On the structure of Painlevé transcendents with a large parameter. II
- Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
- WKB analysis of Painlevé transcendents with a large parameter. I
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