On the Bنcklund 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 [13–17] 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.