On integrable conservation laws

Arsie, Alessandro, Lorenzoni, Paolo and Moro, Antonio (2014) On integrable conservation laws. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471 (201401). ISSN 1471-2946

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Official URL: http://dx.doi.org/10.1098/rspa.2014.0124


We study normal forms of scalar integrable dispersive (non necessarily Hamiltonian) conservation laws via the Dubrovin-Zhang perturbative scheme. Our computations support the conjecture that such normal forms are parametrised by infinitely many arbitrary functions that can be identified with the coefficients of the quasilinear part of the equation. More in general, we conjecture that two scalar integrable evolutionary PDEs having the same quasilinear part are Miura equivalent. This conjecture is also consistent with the tensorial behaviour of these coefficients under general Miura transformations.

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Dr Antonio Moro
Date Deposited: 04 Dec 2014 09:54
Last Modified: 17 Dec 2023 15:33
URI: https://nrl.northumbria.ac.uk/id/eprint/17092

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