ON INTEGRABLE AND SUPER-INTEGRABLE SYSTEMS WITH EXPLICIT X-DEPENDENCE- AN ADLER-KOSTANT-SYMES APPROACH

Explicitly X-dependent integrable equations are obtained by using the AKS theorem in the loop algebraic setting of the SL(2,C) algebra and i ts super-extension. The Hamiltonian structures of these equations are also deduced and discussed, by using Dirac reduction. The supersymmetr ic KdV equation with explicit X-dependence is deduced and shown to be completely integrable. In the whole analysis we have not assumed any n ontrivial variation of the spectral parameter with respect to space or time. (C) 1998 Elsevier Science B.V.