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

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

2010-02-04

arxiv.org/abs/1002.1042v2

Nonlinearity 23:2501,2010

Mathematics

Classical Analysis and ODEs

8 pages, 2 figures

Scientific paper

10.1088/0951-7715/23/10/008

Poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

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