On a reduction of the generalized Darboux-Halphen system

Author(s)

Chanda, Sumanto ^[1] ; Chakravarty, Sarbarish ^[2] ; Guha, Partha ^{[1, 3]}

Affiliation

^[1] SN Bose Natl Ctr Basic Sci, Sect 3, JD Block, Kolkata 700098, W Bengal - India

^[2] Univ Colorado, Dept Math, Colorado Springs, CO 80918 - USA

^[3] IHES, 35 Route Chartres, F-91440 Bures Sur Yvette - France

• Document type: Journal article
• Source: Physics Letters A; v. 382, n. 7, p. 455-460, FEB 20 2018.
• Web of Science Citations: 1

Abstract

The equations for the general Darboux-Halphen system obtained as a reduction of the self-dual Yang Mills can be transformed to a third-order system which resembles the classical Darboux-Halphen system with a common additive terms. It is shown that the transformed system can be further reduced to a constrained non-autonomous, non-homogeneous dynamical system. This dynamical system becomes homogeneous for the classical Darboux-Halphen case, and was studied in the context of self-dual Einstein's equations for Bianchi IX metrics. A Lax pair and Hamiltonian for this reduced system is derived and the solutions for the system are prescribed in terms of hypergeometric functions. (C) 2017 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 16/06560-6 - Nonlinear dynamics and gravity
• Grantee: Betti Hartmann
• Support Opportunities: Research Grants - Visiting Researcher Grant - International