Non-integrability of the Sasano system of type A⁽²⁾₅

2025/12/01 by Tsvetana Stoyanova, Stoyanova, Tsvetana
Mathematics · Physics and Astronomy · #34M40 #34M55 #37J65 #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2512.01767

openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

The Sasano sytem of type A⁽²⁾₅ is a four-dimensional non-linear system of ordinary differential equations, which has an affine Weyl group of symmetries of type A⁽²⁾₅. It is also a tipe dependent Hamiltonian system, which can be considered as coupled Painlevé III systems. In this paper, utilizing the Morales-Ramis-Simó theory for integrability of Hamiltonian systems, we prove rigorously that for all values of the parameters, for which the Sasano system of type A⁽²⁾₅ admits a particular rational solution, it is non-integrable by rational first integrals.

Citations

• Non-integrability of the Painlevé IV equation in the Liouville-Arnold sense and Stokes phenomena
• Introduction to the Galois Theory of Linear Differential Equations
• Higher order Painleve system of type D⁽¹⁾_2n+2 arising from integrable hierarchy

Related

• Non-integrability of the rational Sasano system of type A⁽²⁾₄
• Non-integrability of the Painlevé IV equation in the Liouville-Arnold sense and Stokes phenomena
• Non-integrability of a Hamiltonian system and Legendre functions
• On the algebraic non-integrability of the Halphen system
• Non-integrability of a system with the Dyson Potential