Nahm Equations - Equations

Equations

Let T₁(z),T₂(z), T₃(z) be three matrix-valued meromorphic functions of a complex variable z. The Nahm equations are a system of matrix differential equations

together with certain analyticity properties, reality conditions, and boundary conditions. The three equations can be written concisely using the Levi-Civita symbol, in the form

More generally, instead of considering N by N matrices, one can consider Nahm's equations with values in a Lie algebra g.