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- Title
Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit.
- Authors
Cariñena, José F.; Guha, Partha; Rañada, Manuel F.
- Abstract
We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on S 1 , which in turn is related to the stability algebra of Virasoro orbit. Using Darboux integrability method, we obtain the first integral of the SORE and the results are applied to the study of its Lagrangian and Hamiltonian descriptions. Using these results, we show the existence of a Lagrangian description for SORE, and the Painlevé II equation is analyzed.
- Subjects
PAINLEVE equations; ORBITS (Astronomy); VECTOR fields; RICCATI equation; ALGEBRA
- Publication
Reviews in Mathematical Physics, 2023, Vol 35, Issue 7, p1
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X23300042