Exterior differential systems and Euler-Lagrange partial differential equations

"In the classical calculus of variations, one studies functionals of the form FL(z) = L(x,z, z) dx, Rn, where x = (x1,...,xn), dx = dx1 ... dxn, z = z(x) C1( ) (for example), and the Lagrangian L = L(x,z,p) is a smooth function of x, z, and p = (p1,...,pn)."