Higher local conservation laws for nonlinear sigma models on symmetric spaces

We show that for the classical two-dimensional nonlinear -model on a Riemannian symmetric space of dimensionm and rankp, there existp independent series of higher local conservation laws, and we reduce the field equations of the model to a system of nonlinear partial differential equations possessing an associated Lax pair and involvingm+p independent variables.Dedicated to the Memory of our Colleague and Friend Jorge André SwiecaWork partially done under DFG contract Schr 4/5