H. Aratyn ; J. F. Gomes ; G. V. Lobo ; A. H. Zimerman - Two-fold degeneracy of a class of rational Painlevé V solutions

ocnmp:13201 - Open Communications in Nonlinear Mathematical Physics, April 15, 2024, Proceedings: OCNMP Conference, Bad Ems (Germany), 23-29 June 2024 - https://doi.org/10.46298/ocnmp.13201
Two-fold degeneracy of a class of rational Painlevé V solutionsArticle

Authors: H. Aratyn ; J. F. Gomes ; G. V. Lobo ; A. H. Zimerman

    We present a construction of a class of rational solutions of the Painlevé V equation that exhibit a two-fold degeneracy, meaning that there exist two distinct solutions that share identical parameters. The fundamental object of our study is the orbit of translation operators of $A^{(1)}_{3}$ affine Weyl group acting on the underlying seed solution that only allows action of some symmetry operations. By linking points on this orbit to rational solutions, we establish conditions for such degeneracy to occur after involving in the construction additional Bäcklund transformations that are inexpressible as translation operators. This approach enables us to derive explicit expressions for these degenerate solutions. An advantage of this formalism is that it easily allows generalization to higher Painlevé systems associated with dressing chains of even period $N>4$.


    Volume: Proceedings: OCNMP Conference, Bad Ems (Germany), 23-29 June 2024
    Published on: April 15, 2024
    Accepted on: April 11, 2024
    Submitted on: March 8, 2024
    Keywords: Nonlinear Sciences - Exactly Solvable and Integrable Systems

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