DISCRETIZING FAMILIES OF LINEARIZABLE EQUATIONS

We investigate generalizations of the discrete Riccati equation as a l inearizable system, to multicomponent linearizable systems. These are discretizations of nonlinear ordinary differential equations with supe rposition formulas. We present discrete matrix Riccati equations, proj ective, conformal, orthogonal and symplectic Riccati equations. Also o btained are discrete equations, based on complex orthogonal and symple ctic groups, that in the continuous limit involve fourth order polynom ial nonlinearities. All these equations satisfy the criterion of singu larity confinement. (C) 1998 Published by Elsevier Science B.V.