Lagrangian extensions of multi-dimensional integrable equations. I. The five-dimensional Mart{\'ı}nez Alonso--Shabat equation

I. S. Krasil'shchik, O. I. Morozov

We study a Lagrangian extension of the 5d Martínez Alonso--Shabat equation $\mathcal{E}$ \begin{equation*} u_{yz}=u_{tx}+u_y\,u_{xs}-u_x\,u_{ys} \end{equation*} that coincides with…