Pavel Winternitz - Nonlinear differential and difference equations with superposition formulas

A class of nonlinear ordinary differential equations exists for which the general solution can be written as a function of a finite number of particular solutions. The equations and the superposition formulas are based on transitive effective Lie group actions on homogeneous manifolds. The equations can be discretized to obtain difference equations that also allow superposition formulas. These equations are linearizable by an embedding into a higher-dimensional space. They occur as Backlund transformations in the theory of integrable systems.