Conservation Laws of Second Order for the Born–Infeld Equation and Other Related Equations

We describe a class of quasilinear partial differential equations of second order with two independent variables in the general case of mixed type for which we construct conservation laws of second order which are quadratic with respect to the second derivatives. As examples, we present similar conservation laws for the Born–Infeld equation, for the equations of minimal and maximal surfaces in Minkowski space, and for the classical equation of minimal surfaces.