Superposition formulas for nonlinear superequations. (English) Zbl 0726.58065
Summary: Nonlinear superequations, for which the general solution can be expressed algebraically in terms of a finite number of particular solutions, are obtained. They are based on the orthosymplectic supergroup OSP(m,2n) and its action on a homogeneous superspace. Superposition formulas are discussed for the cases \(m=1\), n arbitrary, and \(m=2\), \(n=1\). For OSP(2,2) the number of particular solutions needed to reconstruct the general solution depends on the dimension of the underlying Grassmann algebra, whereas for OSP(1,2n) it does not.
MSC:
| 58Z05 | Applications of global analysis to the sciences |
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 37N99 | Applications of dynamical systems |
Keywords:
nonlinear superequations; supersymmetry; superposition formula; supergroup; Grassmann algebraReferences:
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