Introduced by Richard S. Ward, the integrable chiral model or Ward model is described in terms of a matrix-valued field J : R 3 → → U ( n ) and is given by the partial differential equation ∂ ∂ t ( J − − 1 J t ) − − ∂ ∂ x ( J − − 1 J x ) − − ∂ ∂ y ( J − − 1 J y ) − − [ J − − 1 J t , J − − 1 J y ] = 0. It has a Lagrangian formulation with the expected kinetic term together with a term which resembles a Wess–Zumino–Witten term. It also has a formulation which is formally identical to the Bogomolny equations but with Lorentz signature. The relation between these formulations can be found in Dunajski (2010).