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Systematic construction of nonautonomous Hamiltonian equations of Painlevé-type. II. Isomonodromic Lax representation


[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[7.4] Mathematics

Year of publication


Published in

Studies in Applied Mathematics

Journal year: 2022 | Journal volume: vol. 149 | Journal number: iss. 2

Article type

scientific article

Publication language


  • Frobenius integrability
  • Lax representation
  • nonautonomous Hamiltonian equations
  • Painlevé equations
  • Stäckel systems

EN This is the second article in a suite of articles investigating relations between Stäckel-type systems and Painlevé-type systems. In this paper, we construct isomonodromic Lax representations for Painlevé-type systems found in the previous paper by Frobenius integrable deformations of Stäckel-type systems. We first construct isomonodromic Lax representations for Painlevé-type systems in the so-called magnetic representation and then, using a multitime-dependent canonical transformation, we also construct isomonodromic Lax representations for Painlevé-type systems in the nonmagnetic representation. Thus, we prove that the Frobenius integrable systems constructed in Part I are indeed of Painlevé-type. We also present isomonodromic Lax representations for all one-, two-, and three-dimensional Painlevé-type systems originating in our scheme. Based on these results we propose complete hierarchies of PI - PIV that follow from our construction.

Pages (from - to)

364 - 415




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