2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95948Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/09_98abs.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).5 pages, AMS-LaTeX. v2: minor correctionsDifferential GeometryHigh Energy Physics - TheoryMathematical PhysicsAnalysis of PDEsExactly Solvable and Integrable Systemstext