Equations with an infinite number of explicit Conservation Laws
Abstract
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved charge densities are all homogeneous polynomials 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 some members of this class possess identical charge densities. This enables the construction of a set of multivariable equations with an infinite number of conservation laws.
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