Second-order integrable Lagrangians and WDVV equations

Evgeny V. Ferapontov, Maxim V. Pavlov, Lingling Xue

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…