Poles of Integrale Tritronquee and Anharmonic Oscillators. A WKB Approach

Abstract

Poles of solutions to the Painleve-I equation are intimately related to the theory of the cubic anharmonic oscillator. In particular, poles of integrale tritronquee are in 1-1 correspondence with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We analyze this pair of quantization conditions by means of a suitable version of the complex WKB method.

26 pages + 2 appendices, 4 figures; Added references; Corrected typos in the text and in equation (39)

References in corpus (1)

• Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis

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