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Equations with an infinite number of explicit conservation laws

Published online by Cambridge University Press:  14 November 2011

D. B. Fairlie
D. B. Fairlie
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, U.K
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 1 , 1997 , pp. 11 - 19
Copyright
Copyright © Royal Society of Edinburgh 1997

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