Some Remarks on Multisymplectic and Variational Nature of Monge-Ampère Equations in Dimension Four

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Authors	SUCHÁNEK Radek
Year of publication	2023
Type	Chapter of a book
MU Faculty or unit	Faculty of Science
Citation
Description	We describe a necessary condition for the local solvability of the strong inverse variational problem in the context of Monge-Ampere partial differential equations and first-order Lagrangians. This condition is based on comparing effective differential forms on the first jet bundle. To illustrate and apply our approach, we study the linear Klein-Gordon equation, first and second heavenly equations of Plebański, Grant equation, and Husain equation, over a real four-dimensional manifold. Two approaches towards multisymplectic formulation of these equations are described.
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