ON CONNECTION FORMULAS FOR THE SECOND PAINLEVÉ TRANSCENDENT. PROOF OF THE MILES CONJECTURE, AND A QUANTIZATION RULE

DOI10.1070/IM1994v042n03ABEH001544zbMath0815.34046OpenAlexW2026507786WikidataQ122925765 ScholiaQ122925765MaRDI QIDQ4319669

A. V. Pereskokov, Mikhail V. Karasev

Publication date: 20 February 1995

Published in: Russian Academy of Sciences. Izvestiya Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im1994v042n03abeh001544

zbMATH Keywords

eigenvaluesturning pointconnection formulassmall parameter multiplying the derivativeglobal asymptotic solutionsMiles conjectureone-dimensional nonlinear Sturm-Liouville equationsolution of KLW type

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Sturm-Liouville theory (34B24) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) General quantum mechanics and problems of quantization (81S99) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (2)

One-dimensional equations of a self-consistent field with cubic nonlinearity in quasiclassical approximation ⋮ On an exact WKB approach to Ablowitz-Segur's connection problem for the second Painlevé equation

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