Symmetries and hamiltonians of Ince's XXXVIII and XLIX equations

Abstract

We discuss symmetries of Hamiltonians of I${}_{38}$ and I${}_{49}$ equations that appear on Ince's list of fifty second-order differential equations with Painlevé property. This study is informed by structure of Weyl symmetries of Painlevé P${}_{III}$ and mixed Painlevé P${}_{III-V}$ equations and provides insights into differences between the symmetries of Painlevé equations and symmetries of solvable equations on Ince's list.

9 pages, Proc. of the 32nd International Colloquium on Group Theoretical Methods in Physics (Group32), 2018, Prague, Czech Republic

References in corpus (1)

• On special limits of the Mixed Painlevé P${}_{\mathbf{III}-\mathbf{V}}$ Model

Cited by in corpus (2)

• Gauge Symmetry Origin of Bäcklund Transformations for Painlevé Equations
• Coalescence, Deformation and Bäcklund Symmetries of Painlevé IV and II Equations