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Extrinsic geometry of differential equations and Green's formula
V. V. Zharinov
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.
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Mathematics of the USSR-Izvestiya, 1990, 35:1, 37–60
MSC: Primary 35A30, 26B20; Secondary 35L65, 58G37, 58A25, 53C85, 35G15, 35G20
V. V. Zharinov, “Extrinsic geometry of differential equations and Green's formula”, Izv. Akad. Nauk SSSR Ser. Mat., 53:4 (1989), 708–730; Math. USSR-Izv., 35:1 (1990), 37–60
Citation in format AMSBIB
\paper Extrinsic geometry of differential equations and Green's formula
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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This publication is cited in the following articles:
V. V. Zharinov, “On spectral sequences of evolution systems with constraints”, Russian Acad. Sci. Sb. Math., 79:1 (1994), 33–45
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