Abstract
Systems of nonlinear ordinary differential equations are constructed, for which the general solution is algebraically expressed in terms of a finite number of particular solutions. Expressions of that type are called nonlinear superposition formulae. These systems are connected with local Lie group transformations on their homogeneous spaces. In the work presented here, the nonlinear superposition formulae are constructed for the case of the SO(3,2) group and some aspects of the general case of SO(n + 1, n) are studied.
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