On the integrability conditions for some structures related to evolution differential equations

Alexander Verbovetsky; Iosif Krasil'shchik; Paul Kersten

arxiv: math/0310451 · v2 · submitted 2003-10-29 · 🧮 math.DG · hep-th· math-ph· math.AP· math.MP· nlin.SI

On the integrability conditions for some structures related to evolution differential equations

Paul Kersten , Iosif Krasil'shchik , Alexander Verbovetsky This is my paper

classification 🧮 math.DG hep-thmath-phmath.APmath.MPnlin.SI

keywords differentialevolutionrespvariationalapplbivectorconditionsdiffiety

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Using 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).

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On the integrability conditions for some structures related to evolution differential equations

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