This article is cited in 5 papers

Essential Conservation Laws for Equations with Infinite Symmetries

V. Rosenhaus

California State University, Chico

Abstract: We consider partial differential equations of variational problems with infinite symmetry groups. We study local conservation laws associated with arbitrary functions of one variable in the group generators. We show that only symmetries with arbitrary functions of dependent variables lead to an infinite number of conservation laws. We also calculate local conservation laws for the potential Zabolotskaya–Khokhlov equation for one of its infinite subgroups.

Keywords: infinite symmetries, conservation laws.

DOI: 10.4213/tmf1845

 English version: Theoretical and Mathematical Physics, 2005, 144:1, 1046–1053

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