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

By Stephen C. Anco, George Bluman. European journal of applied mathematics, 2001

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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.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics

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In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

Direct construction method for conservation laws of partial differential equations Part II: General treatment (2001, methodology): “This paper gives a general treatment and proof of the direct conservation law method presented in Part I (see [3]).”