On the Bäcklund transformations of the Riccati equation: The differential-geometric approach revisited

Making use of well-known results [[3], [5]]and newly discovered differential-geometric properties of adjoint pairs of differential Lax type operators [[13], [14], [15], [16], [17]] corresponding to Riccati-Abel equations, we construct novel generalized Bäcklund transformations for the classical canonical Riccati equation. In addition we prove some new results concerning solutions to generalized Riccati equations.