Geodesic
Extrinsic geometry of differential equations and Green's formula
Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 37-60

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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. 
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     author = {V. V. Zharinov},
     title = {Extrinsic geometry of differential equations and {Green's} formula},
     journal = {Izvestiya. Mathematics },
     pages = {37--60},
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     number = {1},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a1/}
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V. V. Zharinov. Extrinsic geometry of differential equations and Green's formula. Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 37-60. http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a1/