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

José F. Cariñena; Partha Guha; Manuel F. Rañada

doi:10.1142/S0129055X23300042

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

José F. Cariñena, Partha Guha, Manuel F. Rañada

Research output: Contribution to journal › Review article › peer-review

Abstract

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 Painlevé II equation is analyzed.

Original language	British English
Article number	2330004
Journal	Reviews in Mathematical Physics
Volume	35
Issue number	7
DOIs	https://doi.org/10.1142/S0129055X23300042
State	Published - 1 Aug 2023

Keywords

bi-Lagrangian system
Bures equation
Chazy equation
Darboux polynomial
master symmetry
Painlevé II
projective vector field
Riccati

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@article{5a277056ad6840438ff1ab17db9d60bc,

title = "Painlev{\'e} equations, integrable systems and the stabilizer set of Virasoro orbit",

abstract = "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 Painlev{\'e} II equation is analyzed.",

keywords = "bi-Lagrangian system, Bures equation, Chazy equation, Darboux polynomial, master symmetry, Painlev{\'e} II, projective vector field, Riccati",

author = "Cari{\~n}ena, {Jos{\'e} F.} and Partha Guha and Ra{\~n}ada, {Manuel F.}",

note = "Publisher Copyright: {\textcopyright} 2023 World Scientific Publishing Company.",

year = "2023",

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language = "British English",

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TY - JOUR

T1 - Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit

AU - Cariñena, José F.

AU - Guha, Partha

AU - Rañada, Manuel F.

PY - 2023/8/1

Y1 - 2023/8/1

N2 - 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 Painlevé II equation is analyzed.

AB - 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 Painlevé II equation is analyzed.

KW - bi-Lagrangian system

KW - Bures equation

KW - Chazy equation

KW - Darboux polynomial

KW - master symmetry

KW - Painlevé II

KW - projective vector field

KW - Riccati

UR - http://www.scopus.com/inward/record.url?scp=85171743967&partnerID=8YFLogxK

U2 - 10.1142/S0129055X23300042

DO - 10.1142/S0129055X23300042

M3 - Review article

AN - SCOPUS:85171743967

SN - 0129-055X

VL - 35

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 7

M1 - 2330004

ER -

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

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Keywords

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