Seminar talk, 1 February 2012

Speaker: Dmitry Tunitsky

Title: On reduction of quasilinear systems to a block triangular form

Abstract:
The talk will discuss systems of quasilinear partial differential equations of first order with two independent variables. For such systems there is (going back to G.F.B Riemann) geometric formalization that takes the quasilinear system to a field of linear operators on a corresponding vector bundle. In terms of this field we will formulate a number of conditions of reducibility of quasilinear systems to triangular and block triangular form, which extend the results by Haanties and Bogoyavlensky on diagonalization and block diagonalization.