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.

中文翻译：

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广义Kovalevskaya形式的方程组的可拓辛结构与变分学的反问题。

本文致力于微分方程系统的辛结构和变分原理之间的关系。描述了一种用于从合适的辛结构中获得全局变分原理的方法。讨论了该结果与变异演算逆问题的关系。结果表明，演化方程系统的每一个变分形式都与一种特殊形式的总导数中的两面可逆算符有关。