Algebraic construction of integrable and super integrable hierarchies

A general construction of integrable hierarchies based on affine Lie algebras is presented. The models are specified according to some algebraic data and their time evolution is obtained from solutions of the zero curvature condition. Such framework provides an unified treatment of relativistic and non relativistic models. The extension to the construction of supersymmetric integrable hierarchies is proposed. An explicit example of N=2 super mKdV and sinh–Gordon is presented.