On a reduction of the generalized Darboux–Halphen system

Sumanto Chanda, Sarbarish Chakravarty, Partha Guha

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12 Scopus citations

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.

Original languageBritish English
Pages (from-to)455-460
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume382
Issue number7
DOIs
StatePublished - 20 Feb 2018

Keywords

  • Bianchi-IX
  • Darboux–Halphen
  • Hypergeometric function
  • Lax representation
  • Self-dual Yang–Mills

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