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Zbl 1034.35070
Anco, Stephen C.; Bluman, George
Direct construction method for conservation laws of partial differential equations. I: Examples of conservation law classifications. (English)
[J] Eur. J. Appl. Math. 13, No. 5, 545-566 (2002). ISSN 0956-7925; ISSN 1469-4425/e

In the authors' works [Phys. Rev. Lett. 78, 2869--2873 (1997; Zbl 0948.58015), Eur. J. Appl. Math. 9, 245--259 (1998; Zbl 0922.34006)] the authors have presented an algorithmic approach replacing Noether's theorem allowing to obtain all local conservation laws for any differential equations, especially for ordinary ones, whether or not they have variational principles. Here they concentrate on partial differential equations. This method reduces the computation of conservation laws to solving a system of linear determining equations similar to those for finding symmetries. It gives an explicit construction formula yielding a conservation law for each solution of the determining system. Part 1 presents examples of nonlinear wave equations to exhibit the method and classification results for conservation laws of these equations. For Part 2 see the review Zbl 1034.35071 below.
[Boris V. Loginov (Ulyanovsk)]

MSC 2000:: *35L65 Conservation laws
58J70 Invariance and symmetry properties

Keywords: partial differential equations; symmetry; conservation laws, algorithmic approach.

Citations: Zbl 0948.58015; Zbl 1034.35071; Zbl 0922.34006

Cited in: Zbl 1034.35071

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