A linear-algebraic method to compute polynomial PDE conservation laws

We present a method to compute polynomial conservation laws for systems of partial differential equations ( PDE s). The method only relies on linear algebraic computations and is complete, in the sense it can find a basis for all polynomial fluxes that yield conservation laws, up to a specified order of derivatives and degree. We compare our method to state-of-the-art algorithms based on the direct approach on a few PDE systems drawn from mathematical physics.