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The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation.
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I. Anderson and G. Thompson, The inverse problem of the calculus of variations for ordinary differential equations · 1992
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T. J. Bridges, P. E. Hydon, and J. K. Lawson, “Multisymplectic structures and the variational bicomplex,” Mathematical Proceedings of the Cambridge Philosophical Society
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