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A method for symbolically computing conservation laws of nonlinear partialdifferential equations (PDEs) in multiple space dimensions is presented in thelanguage of variational calculus and linear algebra. The steps of the methodare illustrated using the Zakharov-Kuznetsov and Kadomtsev-Petviashviliequations as examples. The method is algorithmic and has been implemented inMathematica. The software package, ConservationLawsMD.m, can be used tosymbolically compute and test conservation laws for polynomial PDEs that can bewritten as nonlinear evolution equations. The code ConservationLawsMD.m hasbeen applied to (2+1)-dimensional versions of the Sawada-Kotera, Camassa-Holm,and Gardner equations, and the multi-dimensional Khokhlov-Zabolotskayaequation.

Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions