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Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classifications

Published online by Cambridge University Press:  28 November 2002

STEPHEN C. ANCO  and
GEORGE BLUMAN
STEPHEN C. ANCO
Affiliation:
Department of Mathematics, Brock University, St. Catharines, ON Canada L2S 3A1 email: sanco@brocku.ca
GEORGE BLUMAN
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC Canada V6T 1Z2 email: bluman@math.ubc.ca
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Abstract

An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a variational principle and reduces the calculation of conservation laws to solving a system of linear determining equations similar to that for finding symmetries. An explicit construction formula is derived which yields a conservation law for each solution of the determining system. In the first of two papers (Part I), examples of nonlinear wave equations are used to exhibit the method. Classification results for conservation laws of these equations are obtained. In a second paper (Part II), a general treatment of the method is given.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 5 , October 2002 , pp. 545 - 566
Copyright
2002 Cambridge University Press

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