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arXiv · 2012.07321

Elliptic asymptotic representation of the fifth Painlev\'e transcendents

Shun Shimomura
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Abstract

For the fifth Painlev\'e transcendents an asymptotic representation by the Jacobi $\mathrm{sn}$-function is presented in cheese-like strips along generic directions near the point at infinity. Its elliptic main part may be understood to depend on the phase shift as a single integration constant, which is parametrised by monodromy data for the associated isomonodromy deformation. The other integration constant is contained in the error term or in a correction function. This paper contains corrections of the Stokes graph and of the related results in the early version.

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Shun Shimomura. 2020-12-14. Elliptic asymptotic representation of the fifth Painlev\'e transcendents. https://arxiv.org/abs/2012.07321

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