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arXiv · 2009.05219

Coalescence, Deformation and B\"acklund Symmetries of Painlev\'e IV and II Equations

V. C. C. Alves·H. Aratyn·J. F. Gomes·A. H. Zimerman
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Abstract

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

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V. C. C. Alves, H. Aratyn, J. F. Gomes, A. H. Zimerman. 2020-09-11. Coalescence, Deformation and B\"acklund Symmetries of Painlev\'e IV and II Equations. https://doi.org/10.1088/1751-8121%2Fabb725

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