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Analytic Properties of Solutions to Equations in the Generalized Hierarchy of the Second Painlevé Equation

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Abstract

We consider the analytic properties of solutions to equations of arbitrary order in the generalized hierarchy of the second Painlevé equation. The local properties of solutions, the Bäcklund transformations, and rational solutions and their representations via generalized Yablonskii–Vorob’ev polynomials are studied.

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Notes

  1. From now on, \(\beta =(\beta _{1},\ldots ,\beta _{N-1})\) .

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  1. Belarusian State University, Minsk, 220030, Belarus

    V. I. Gromak

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Translated by V. Potapchouck

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Gromak, V.I. Analytic Properties of Solutions to Equations in the Generalized Hierarchy of the Second Painlevé Equation. Diff Equat 56, 993–1009 (2020). https://doi.org/10.1134/S0012266120080030

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