On a class of three-dimensional integrable Lagrangians

E. V. Ferapontov, K. R. Khusnutdinova, S. P. Tsarev

We characterize non-degenerate Lagrangians of the form $\int f(u_x,u_y,u_t)dxdydt$ such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})…