THE MOSER TYPE REDUCTION OF INTEGRABLE RICCATI DIFFERENTIAL EQUATIONS AND ITS LIE-ALGEBRAIC STRUCTURE

A given Riccati equation, as is well known, can be naturally reduced Ato a system of nonlinear evolution equations on an Ainfinite-dimensional functional manifold with Cauchy-Goursat initial Adata. We describe the Lie algebraic reduction procedure of nonlocal Atype for this infinite-dimensional dynamical system upon the set of Acritical points of an invariant Lagrangian functional. As one of our Amain results, we show that the reduced dynamical system generates the Acompletely integrabic Hamiltonian flow on this submanifold with Arespect to the canonical symplectic structure upon it. The above also Amakes it possible to find effectively its finite-dimensional Lax type representation via both the well known Moser type reduction Aprocedure and the dual momentum mapping scheme on some matrix Amanifold.