Abstract
Partial differential equations with supersymmetric (1, 1) time are investigated by means of superspace Cauchy-Kowalewsky and Cartan-Kähler techniques. Theorems for the existence and uniqueness of solutions are found for a particular class of superanalytic functions. The (1, 1) time evolution equations are very important in applications to supersymmetric quantum mechanics and quantum field theory: the square roots of Schrödinger and heat equations. We considered nonlinear analogs of these equations which can be interpreted as square roots of Maslov's nonlinear Schrödinger and heat equations.
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