Systematic construction of nonautonomous Hamiltonian equations of Painleve-type. II. Isomonodromic Lax representation
| Autor: | Krzysztof Marciniak, Maciej Błaszak, Ziemowit Domański |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Nonlinear Sciences - Exactly Solvable and Integrable Systems
Beräkningsmatematik Applied Mathematics Mathematics::Classical Analysis and ODEs FOS: Physical sciences Mathematical Physics (math-ph) Frobenius integrability Lax representation nonautonomous Hamiltonian equations Painleve equations Stackel systems Computational Mathematics Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics Exactly Solvable and Integrable Systems (nlin.SI) 37J35 14H70 70H20 Mathematical Physics |
| Popis: | This is the second article in a suite of articles investigating relations between St\"{a}ckel-type systems and Painlev\'{e}-type systems. In this article we construct isomonodromic Lax representations for Painlev\'{e}-type systems found in the previous paper by Frobenius integrable deformations of St\"{a}ckel-type systems. We first construct isomonodromic Lax representations for Painlev\'{e}-type systems in the so called magnetic representation and then, using a multitime-dependent canonical transformation, we also construct isomonodromic Lax representations for Painlev\'{e}-type systems in the non-magnetic representation. Thus, we prove that the Frobenius integrable systems constructed in Part I are indeed of Painlev\'{e}-type. We also present isomonodromic Lax representations for all one-, two- and three-dimensional Painlev\'{e}-type systems originating in our scheme. Based on these results we propose complete hierarchies of $P_{I}-P_{IV}$ that follow from our construction. Comment: 40 pages |
| Databáze: | OpenAIRE |
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