On the integrability conditions for some structures related to evolution differential equations
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky
Abstract
Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/0998abs.htm), we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with nondegenerate right-hand side is Hamiltonian (resp., symplectic).
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