Some Remarks on Multisymplectic and Variational Nature of Monge-Amp\`ere Equations in Dimension Four
Mathematical Physics
2023-05-05 v1 math.MP
Abstract
We describe a necessary condition for the local solvability of the strong inverse variational problem in the context of Monge-Amp\`ere 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 Pleba\'nski, Grant equation, and Husain equation, over a real four-dimensional manifold. Two approaches towards multisymplectic formulation of these equations are described.
Keywords
Cite
@article{arxiv.2305.02431,
title = {Some Remarks on Multisymplectic and Variational Nature of Monge-Amp\`ere Equations in Dimension Four},
author = {Radek Suchánek},
journal= {arXiv preprint arXiv:2305.02431},
year = {2023}
}