Equivalence of conservation laws and equivalence of potential systems

Details Equivalence of conservation laws and equivalence of potential systems Equivalence of conservation laws and equivalence of potential systems

2006-11-14

arxiv.org/abs/math-ph/0611032v2

Int. J. Theor. Phys., 2007, V.46, 2658--2668

Physics

Mathematical Physics

10 pages

Scientific paper

10.1007/s10773-007-9378-2

We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are considered as examples. Using reducibility of them to the one-dimensional linear heat equation, we construct complete hierarchies of local and potential conservation laws for them and describe, in some sense, all their potential symmetries. Known results on the subject are interpreted in the proposed framework. This paper is an extended comment on the paper of J.-q. Mei and H.-q. Zhang [Internat. J. Theoret. Phys., 2006, in press].

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