Consider the worldsheet in light-cone coordinates x ± ± = t ± ± x . The components of the appropriate Lax matrix are L ± ± ( x + , x − − ; λ λ ) = j ± ± 1 ∓ ∓ λ λ . The requirement that the zero-curvature condition on L ± ± for all λ λ is equivalent to the conservation of current and flatness of the current j = ( j + , j − − ) , that is, the equations of motion from the principal chiral model (PCM).