These results are original contributions in modern algebraic theory of integrable dynamic systems, and they are very important to physics-mathematics, in particular to study soliton type equations. They include new generalizations of mathematical concepts and methods of this theory, and embrace properties of integrable systems of ordinary differential equations (discrete KP hierarchy) and of equations in partial derivatives. Some of these results are the contributions in:

• Algebraic properties of gradient flows: Introduction and study of gradient integrable flows (Brockett type hierarchy) for equations in partial derivatives. A supersymmetrical extension of this hierarchy, which constitutes a first example of graduate gradient flow (with odd variables).
• Study of Lax type equations with several Lie switches.
• Algebraic properties of discreet KP hierarchy: Extension to the discreet case of Mulase method by means of the use of Borel-Gauss type factorizations of bi-infinite matrixes.
• Construction of commutative rings of differential operators in the elliptic case with an arbitrary number of odd variables, with new supersymmetrical extensions of the KdV equation and Schroginger operator.

These results have been published in 6 international prestigious magazines from 1998 to 2001.