International Journal of Theoretical Physics

, Volume 46, Issue 10, pp 2658–2668 | Cite as

Equivalence of Conservation Laws and Equivalence of Potential Systems

  • N. M. Ivanova
  • R. O. Popovych


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 Mei and Zhang [Int. J. Theor. Phys. 45: 2095–2102, 2006].


Burger Equation Planck Equation Partial Differential Equa Potential Equation Point Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institute of Mathematics of NAS of UkraineKievUkraine
  2. 2.Fakultät für MathematikUniversität WienWienAustria

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