Poles of Integrale Tritronquee and Anharmonic Oscillators. A WKB Approach

Details Poles of Integrale Tritronquee and Anharmonic Oscillators. A WKB Approach Poles of Integrale Tritronquee and Anharmonic Oscillators. A WKB Approach

2009-09-30

arxiv.org/abs/0909.5537v2

2010 J. Phys. A: Math. Theor. 43 095201

Mathematics

Classical Analysis and ODEs

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

Scientific paper

10.1088/1751-8113/43/9/095201

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.

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