DIFFERENTIAL-EQUATIONS WITH SUPERSYMMETRIC TIME

Partial differential equations with supersymmetric (1, 1) time are inv estigated by means of superspace Cauchy Kowalewsky and Cartan-Kahler t echniques. Theorems for the existence and uniqueness of solutions are found for a particular class of superanalytic functions. The (1, 1) ti me evolution equations are very important in applications to supersymm etric quantum mechanics and quantum field theory: the square roots of Schrodinger and heat equations. We considered nonlinear analogs of the se equations which can be interpreted as square roots of Maslov's nonl inear Schrodinger and heat equations.