LAUSR

The method of transformation of a linear system of evolution equations into the system of Riccati-type equations is elaborated. It is shown that the system of generalized Riccati equations is governed by the characteristic polynomial of n-order generator matrix of the linear system of evolution equations. Solutions of the generalized Riccati equations are presented by roots of the polynomial function, whose coefficients constitute the solutions of the linear system of evolution equations. An inverse mapping from the solutions of generalized Riccati equations onto the solutions of the linear evolution equations is constructed.