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The Generalized Chazy Equation from the Self‐Duality Equations
Author(s) -
Ablowitz M. J.,
Chakravarty S.,
Halburd R.
Publication year - 1999
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00121
Subject(s) - conformal map , duality (order theory) , piecewise , mathematics , mathematical physics , gauge (firearms) , mathematical analysis , algebra over a field , pure mathematics , archaeology , history
It is shown that classically known generalizations of the Chazy equation and Darboux–Halphen system are reductions of the self‐dual Yang–Mills (SDYM) equations with an infinite‐dimensional gauge algebra. The general ninth‐order Darboux–Halphen system is reduced to a Schwarzian equation which governs conformal mappings of regions with piecewise circular sides. The generalized Chazy equation is shown to correspond to special mappings where either the triangles are equiangular or two of the angles are π/3.