Full characterisation of Painlev\'e V asymptotics and nonlinear monodromy-Stokes structure

Summary · qwen2.5:32b

The study provides a comprehensive characterization of Painlevé V equation asymptotics within a right half-plane near infinity, identifying all possible solutions linked to monodromy data across the entire monodromy manifold. This includes new truncated solutions along imaginary axes and elliptic asymptotics in generic directions, complementing previous work by Andreev and Kitaev. The research also outlines a nonlinear monodromy-Stokes structure that describes changes in monodromy data as part of solution expressions during analytic continuation.

Excerpt

arXiv:2509.01385v3 Announce Type: replace Abstract: For a generic Painlev\'e V equation we characterise all the asymptotics in a right half plane near the point at infinity, that is, we find classified explicit solutions that are, by the Riemann-Hilbert correspondence, labelled with monodromy data filling up the whole monodromy manifold. To do so, in addition to the asymptotics by Andreev and Kitaev along the positive real axis, we require elliptic asymptotics along generic directions and newly provided truncated solutions arising from a general solution along the imaginary axes. To know analytic continuations outside this region we formulate a nonlinear monodromy-Stokes structure, which is observed as changes of monodromy data contained in the explicit expressions of solutions.