Coalescence, Deformation and Bäcklund Symmetries of Painlevé IV and II Equations

Abstract

We extend Painlevé IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlevé IV and II equations for special limits of the underlying parameters. We derive the underlying Bäcklund transformations, symmetry structure and requirements to satisfy Painlevé property.

21 pages, to appear in J. Phys. A: Math. Theor. (2020)

References in corpus (2)

• Symmetries and hamiltonians of Ince's XXXVIII and XLIX equations
• 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
• Extended symmetry of higher Painlevé equations of even periodicity and their rational solutions