The Nahm-Schmid equations and Hypersymplectic Geometry

We explore the geometry of the Nahm-Schmid equations, a version of Nahm's equations in split signature. Our discussion ties up different aspects of their integrable nature: dimensional reduction from the Yang--Mills anti-self-duality equations, explicit solutions, Lax-pair formulation, conservation laws and spectral curves, as well as their relation to hypersymplectic geometry.