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Nonlinear evolution equations with (1,1)-supersymmetric time

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Abstract

A generalization of the Cauchy-Kowalewsky theorem is obtained for nonlinear evolution equations with (1,1)-supersymmetric time. This theorem ensures the existence and uniqueness of a solution for a large class of superanalytic functions. A generalization of Cartan's technique to the supersymmetric case is also obtained, and by means of it the problem of integrating a system of partial differential equations is transformed into the problem of finding a sequence of integral supermanifolds of lower dimension by means of a succession of integrations based on the Cauchy-Kowalewsky theorem. Evolution equations with (1, 1) time are important for applications to supersymmetric quantum mechanics and field theory, namely, square roots of the Schrödinger and heat-conduction equations. We consider nonlinear generalizations of such equations.

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Authors
  1. A. Yu. Khrennikov
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  2. R. Cianci
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Additional information

Moscow Institute of Electronic Technology; University of Genoa. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 2, pp. 238–246, November, 1993.

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Khrennikov, A.Y., Cianci, R. Nonlinear evolution equations with (1,1)-supersymmetric time. Theor Math Phys 97, 1267–1272 (1993). https://doi.org/10.1007/BF01016872

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  • DOI: https://doi.org/10.1007/BF01016872

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