Nonlinear superposition formulas: Some physically motivated examples

Abstract

This paper gives an account of the nonlinear superposition principle for classes of nonlinear systems. The existence of a nonlinear superposition principle is ensured by a Lie algebraic analysis of the nonlinear system, whereas the nonlinear superposition formulas are obtained in closed form by computing some functionally independent first integrals of an auxiliary system that can be associated with the given one.