Second-order integrable Lagrangians and WDVV equations
Exactly Solvable and Integrable Systems
2021-05-12 v1 Mathematical Physics
math.MP
Abstract
We investigate integrability of Euler-Lagrange equations associated with 2D second-order Lagrangians of the form \begin{equation*} \int f(u_{xx},u_{xy},u_{yy})\ dxdy. \end{equation*} By deriving integrability conditions for the Lagrangian density , examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.
Cite
@article{arxiv.2007.03768,
title = {Second-order integrable Lagrangians and WDVV equations},
author = {Evgeny V. Ferapontov and Maxim V. Pavlov and Lingling Xue},
journal= {arXiv preprint arXiv:2007.03768},
year = {2021}
}