Physics – Mathematical Physics
Scientific paper
2001-08-27
Euro. J. Applied Math. 13 (2002) 545-566
Physics
Mathematical Physics
Published version; 23 pages; LaTeX
Scientific paper
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.
Anco Stephen C.
Bluman George
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