Nonlinear superposition formulas based on imprimitive group action

Systems of nonlinear ordinary differential equations are constructed for wh ich the general solution is expressed algebraically in terms of a finite nu mber of particular solutions. The equations and the corresponding nonlinear superposition formula are based on a nonlinear action of the Lie group SL( N, C) on a homogeneous space M. The isotropy group of the origin of this sp ace is a nonmaximal parabolic subgroup of SL(N, C). Such equations can occu r as Backlund transformations for soliton equations on flag manifolds. (C) 1999 American Institute of Physics. [S0022-2488(99)00306-0].