The Cartan – Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders

Abstract

We develop the Cartan – Monge geometric approach to the characteristic method for nonlinear part ial differential equations of the first and higher orders. The Hamiltonian structure of characteristic vector fields related with nonlinear partial differential equations of the first order is analyzed, the tensor fields of special structure are constructed for defining characteristic vector fields naturally related with nonlinear partial differential equations of higher orders.