Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena
Tsvetana Stoyanova
Abstract:In this paper we study the integrability of the Hamiltonian system associated with the fourth Painlevé equation. We prove that one two‐parametric family of this Hamiltonian system is not integrable in the sense of the Liouville–Arnold theorem. Computing explicitly the Stokes matrices and the formal invariants of the second variational equations, we deduce that the connected component of the unit element of the corresponding differential Galois group is not Abelian. Thus the Morales–Ramis–Simó theory leads to a… Show more
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