Non-integrability of the second Painleve equation as a Hamiltonian system
Tsvetana Stoyanova, Ognyan Christov
TL;DR
This paper proves that the second Painleve equation, when viewed as a Hamiltonian system, does not admit any additional rational integrals, indicating its non-integrability.
Contribution
It applies Morales-Ramis theory to establish the non-existence of rational integrals for the second Painleve equation as a Hamiltonian system, providing a rigorous non-integrability proof.
Findings
No additional rational integrals exist for the system.
The second Painleve equation is non-integrable in the rational sense.
Morales-Ramis theory effectively proves non-integrability.
Abstract
We prove non-existence of an additional rational integral for the second Painleve equation considered as a Hamiltonian system using Morales - Ramis theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Quantum chaos and dynamical systems