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

2023/05/03 by Radek Suchánek, Suchánek, Radek
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2305.02431

openalex publication_date 2023/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a necessary condition for the local solvability of the strong inverse variational problem in the context of Monge-Ampère 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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