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 TMF, 1993, Volume 97, Number 2, Pages 238–246 (Mi tmf1736)

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

A. Yu. Khrennikova, R. Ciancib

a Moscow State Institute of Electronic Technology (Technical University)
b University of Genova

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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English version:
Theoretical and Mathematical Physics, 1993, 97:2, 1267–1272

Bibliographic databases:

Citation: A. Yu. Khrennikov, R. Cianci, “Nonlinear evolution equations with (1,1)-supersymmetric time”, TMF, 97:2 (1993), 238–246; Theoret. and Math. Phys., 97:2 (1993), 1267–1272

Citation in format AMSBIB
\Bibitem{KhrCia93} \by A.~Yu.~Khrennikov, R.~Cianci \paper Nonlinear evolution equations with~(1,1)-supersymmetric time \jour TMF \yr 1993 \vol 97 \issue 2 \pages 238--246 \mathnet{http://mi.mathnet.ru/tmf1736} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1257869} \zmath{https://zbmath.org/?q=an:0806.58006} \transl \jour Theoret. and Math. Phys. \yr 1993 \vol 97 \issue 2 \pages 1267--1272 \crossref{https://doi.org/10.1007/BF01016872} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993NK68000006}