Symmetric Conservation Laws

Mark Hickman
Department of Mathematics and Statistics
University of Canterbury
Christchurch, New Zealand         

email: M.Hickman@math.canterbury.ac.nz

The computation of conservation laws that are "invariant" under a given
symmetry is considered.  These conservation laws are characterized as
eigenfunctions of the prolongation of the symmetry.  Under suitable
assumptions, the eigenspace for each eigenvalue is finite dimensional and the
computation reduces to solving a finite system of linear algebraic equations.
These conservation laws are useful in constructing Wahlquist-Estabrook
prolongations of the original system of equations (such that the given symmetry
extends to the prolongation).