Stephen Anco - Conservation laws of field equations

A computationally effective method for finding the local conservation laws of PDEs is presented using adjoint symmetries (i.e. the solutions of the adjoint equation of the determining equation for symmetries). It is shown that for any given PDE(s), all local conservation laws can be constructed by an integral formula in terms of adjoint symmetries satisfying certain conditions. The effectiveness of this approach lies in being able to calculate these adjoint symmetries as solutions of a system of extended determining equations (i.e. the adjoint symmetry determining equation plus the conditions) working just on the solution space of the PDE(s) by an algorithmic procedure similar to calculating symmetries. Some applications to classifying conservation laws of various field equations in mathematical physics are given.