Peter Hydon is visiting the University of British Columbia in Vancouver this week for the conference Symmetry Methods, Applications, and Related Fields, which celebrates the work of George Bluman. Peter is on the Scientific Organizing Committee and will be speaking on “Conservation laws: from differential to difference“.

Abstract: Conservation laws express fundamental properties that are common to every solution of a system of equations. For PDEs, conservation laws may be found directly, by using a method developed by George Bluman and Stephen Anco. If a given system of PDEs is the Euler-Lagrange system associated with a variational problem, one can also use Noether’s two theorems on variational symmetries to extract conservation laws or relations between the PDEs. This talk describes how these ideas extend to partial difference equations. Some of the basic constructions for PDEs can no longer be used. Even so, difference analogues of the direct method and Noether’s theorems have been found, together with a new result that bridges the gap between Noether’s two theorems (for both PDEs and difference equations). The talk concludes with a brief discussion of the reason for the close analogy between conservation law methods for differential and difference equations.