2024/02/22 by Tsvetana Stoyanova, Stoyanova, Tsvetana
Mathematics · Physics and Astronomy · #33C15 #34M55 #37J65 #37M30 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2402.14351
openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the integrability of the Sasano system of type A(2)4 from the point of view of the Hamiltonian dynamics. We prove rigorously that for these values of the parameters for which the Sasano system of type A(2)4 has a particular rational solution it is not integrable by rational first integrals. By an explicit computation we show that the connected component G0 of the unit element of the differential Galois group of the normal variational equations along a simple particular rational solution is a direct product of two groups SL2(ℂ). This the Morales-Ramis theory leads to a non-integrable result. Moreover using Bäcklund transformations we extend the obtained particular non-integrable result to the entire orbit of the parameters.