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arXiv · 1710.00158

On a reduction of the generalized Darboux-Halphen system

Sumanto Chanda·Sarbarish Chakravarty·Partha Guha
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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.

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Sumanto Chanda, Sarbarish Chakravarty, Partha Guha. 2017-09-30. On a reduction of the generalized Darboux-Halphen system. https://doi.org/10.1016/j.physleta.2017.12.034

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