Solutions of nonlinear differential and difference equations with superposition formulas (Q1581087)

The authors demonstrate that matrix Riccati equations with constant coefficients and their group theoretical discretizations have the same solutions. It is shown how other types of equations with superposition formulas (the scalar Riccati equation, coupled Riccati equations based on a nonprimitive group action, projective Riccati equations) can be discretized via an integration of the underlying vector fields. For the case of constant coefficients the continuous and discrete equations have the same solutions.