Symbolic Representation and Classification of N = 1 Supersymmetric Evolutionary Equations

We extend the symbolic representation to the ring of N = 1 supersymmetricdifferential polynomials, and demonstrate that operations on the ring, suchas the super derivative, Fr´echet derivative, and super commutator, can becarried out in the symbolic way. Using the symbolic representation, weclassify scalar ?-homogeneous N = 1 supersymmetric evolutionary equa-tions with nonzero linear term when ?>0 for arbitrary order and give acomprehensive description of all such integrable equations.