Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions. (English) Zbl 1234.35071
Summary: A method for symbolically computing conservation laws of nonlinear partial differential equations (PDEs) in multiple space dimensions is presented in the language of variational calculus and linear algebra. The steps of the method are illustrated using the Zakharov-Kuznetsov and Kadomtsev-Petviashvili equations as examples.The method is algorithmic and has been implemented in Mathematica. The software package, ConservationLawsMD.m, can be used to symbolically compute and test conservation laws for polynomial PDEs that can be written as nonlinear evolution equations. The code ConservationLawsMD.m has been applied to multi-dimensional versions of the Sawada-Kotera, Camassa-Holm, Gardner, and Khokhlov-Zabolotskaya equations.
MSC:
| 35G20 | Nonlinear higher-order PDEs |
| 68W30 | Symbolic computation and algebraic computation |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
conservation laws; nonlinear PDEs; symbolic software; complete integrability; Kadomtsev-Petviashvili equations; software packageSoftware:
GeM; Mathematica; HomotopyIntegrator; DifferentialGeometry; ConservationLawsMD; Vessiot; PDEtools; PDERecursionOperatorReferences:
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