Extrinsic geometry of differential equations and Green's formula

In the framework of the geometric theory of differential equations the case is considered when the equation under study is a reduction of a broader ambient equation, and the extrinsic geometry arising in this case is investigated. A mapping is constructed with kernel describing the infinitesimal symmetries of the equation under study, along with a dual mapping with kernel containing the characteristics of the conservation laws of the equation. It is shown that the equality expressing this duality in the situation arising from a system of nonlinear partial differential equations becomes the Green's formula for this system. A construction is given for the characteristic mapping that associates with each conservation law of the equation its characteristic.
Bibliography: 13 titles.