NUMERICAL-SOLUTION OF ISOSPECTRAL FLOWS

In this paper we are concerned with the problem of solving numerically isospectral flows. These flows are characterized by the differential equation L' = [B(L),L], L(0) = L-0, where L-0 is a d x d symmetric mat rix, B(L) is a skew-symmetric matrix function of L and [B,L] is the Li e bracket operator. We show that standard Runge-Kutta schemes fail in recovering the main qualitative feature of these flows, that is isospe ctrality, since they cannot recover arbitrary cubic conservation laws. This failure motivates us to introduce an alternative approach and es tablish a framework for generation of isospectral methods of arbitrari ly high order.