Symmetry invariance of conservation laws

Stephen C. Anco, Abdul H. Kara

Published 2015-10-30Version 1

Symmetry invariance of conservation laws of partial differential equations is developed and applied to several examples by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law and its associated conserved quantity are invariant (and, more generally, homogeneous) under the action of a symmetry. These results are used to show that a recent conservation law formula (due to Ibragimov) is equivalent to a standard formula for the action of an infinitesimal symmetry on a conservation law multiplier.