We present a method to compute polynomial conservation laws for systems of partial differential equations (PDEs). 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. (C) 2021 Elsevier Ltd. All rights reserved.
A linear-algebraic method to compute polynomial PDE conservation laws / Boreale, M; Collodi, L. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - STAMPA. - 108:(2022), pp. 55-72. [10.1016/j.jsc.2021.06.003]
A linear-algebraic method to compute polynomial PDE conservation laws
Boreale, M;Collodi, L
2022
Abstract
We present a method to compute polynomial conservation laws for systems of partial differential equations (PDEs). 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. (C) 2021 Elsevier Ltd. All rights reserved.
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