EQUATIONS WITH AN INFINITE NUMBER OF EXPLICIT CONSERVATION-LAWS

A large class of first-order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomi al conservation laws derived from an explicit generating function is c onstructed. The conserved charge densities are all homogeneous polynom ials in the unknown functions which satisfy the differential equations in question. The simplest member of the class of equations is related to the Born-Infeld Equation in two dimensions. It is observed that so me members of this class possess identical charge densities. This enab les the construction of a set of multivariable equations with an infin ite number of conservation laws.