SUPERPOSITION FORMULAS FOR NONLINEAR SUPEREQUATIONS

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. © 1990 American Institute of Physics.