Poles of Integrale Tritronquee and Anharmonic Oscillators. A WKB Approach

Understand

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.