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

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

On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt. 1

The geometric structure of characteristic surfaces related with partial differential equations of first and higer orders is studied making use the vector field technique on hypersurfaces. It is shown, that corresponding characteristics are defined uniquely up to some smooth tensor fields, thereby supplying additional information about the suitable set of their solutions. In particular, it may be very useful for studying asymptotic properties of solutions to our partial differential equations under some boundary conditions