Alves, V. C.C. [UNESP]Aratyn, H.Gomes, J. F. [UNESP]Zimerman, A. H. [UNESP]2021-06-252021-06-252020-11-01Journal of Physics A: Mathematical and Theoretical, v. 53, n. 44, 2020.1751-81211751-8113http://hdl.handle.net/11449/206791We 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.engBacklund transformationsCoalescencePainleve equationsSymmetriesArtigo10.1088/1751-8121/abb7252-s2.0-85095420033