Extendable symplectic structures and the inverse problem of the calculus of variations for systems of equations written in generalized Kovalevskaya formстатья
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Дата последнего поиска статьи во внешних источниках: 8 апреля 2021 г.
Аннотация:The paper is devoted to the relation between symplectic structures and variational principles for systems of differential equations. A method for obtaining a global variational principle from a suitable symplectic structure is described. Relation of this result to the inverse problem of the calculus of variations is discussed. It is shown that each variational formulation for a system of evolution equations is related to a two-sided invertible operator in total derivatives of a special form.