Coalescence, deformation and Bäcklund symmetries of Painlevé IV and II equations. (English) Zbl 1519.34105
Summary: 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.
MSC:
| 34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
| 37J65 | Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) |
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