Geodesic
Nonlinear evolution equations with~(1,1)-supersymmetric time
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 238-246

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_1993_97_2_a5,
     author = {A. Yu. Khrennikov and R. Cianci},
     title = {Nonlinear evolution equations with~(1,1)-supersymmetric time},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {238--246},
     publisher = {mathdoc},
     volume = {97},
     number = {2},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a5/}
}
TY  - JOUR
AU  - A. Yu. Khrennikov
AU  - R. Cianci
TI  - Nonlinear evolution equations with~(1,1)-supersymmetric time
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 238
EP  - 246
VL  - 97
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a5/
LA  - ru
ID  - TMF_1993_97_2_a5
ER  - 
%0 Journal Article
%A A. Yu. Khrennikov
%A R. Cianci
%T Nonlinear evolution equations with~(1,1)-supersymmetric time
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 238-246
%V 97
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a5/
%G ru
%F TMF_1993_97_2_a5
A. Yu. Khrennikov; R. Cianci. Nonlinear evolution equations with~(1,1)-supersymmetric time. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 238-246. http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a5/