Painleve equations, integrable systems and the stabilizer set of Virasoro orbit

被引：0
|
作者：
Carinena, Jose F. [1 ,2 ]
Guha, Partha [3 ,4 ]
Ranada, Manuel F. [1 ,2 ]
机构：
[1] Univ Zaragoza, Dept Fis Teor, Zaragoza 50009, Spain
[2] Univ Zaragoza, Inst Univ Matemat & Aplicac IUMA, Zaragoza 50009, Spain
[3] Khalifa Univ Sci & Technol, Dept Math, Zone 1 Main Campus POB 127788, Abu Dhabi, U Arab Emirates
[4] SN Bose Natl Ctr Basic Sci, JD Block Sect 3, Kolkata 700106, India
来源：
REVIEWS IN MATHEMATICAL PHYSICS | 2023年 / 35卷 / 07期
关键词：
Riccati; projective vector field; Darboux polynomial; master symmetry; bi-Lagrangian system; Painleve II; Chazy equation; Bures equation; ORDINARY DIFFERENTIAL-EQUATIONS; LIE SYSTEMS; POLYNOMIAL HAMILTONIANS; GEODESIC-FLOWS; 2ND-ORDER; RICCATI; KDV; HIERARCHY; 1ST; S-1;
D O I：
10.1142/S0129055X23300042
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on S1, 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 Painleve II equation is analyzed.
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页数：43
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