title: On integrable conservation laws.
abstract: We study normal forms of scalar integrable dispersive (not necessarily Hamiltonian) conservation laws, via the Dubrovin-Zhang perturbative scheme. Our computations support the conjecture that such normal forms are parametrized by infinitely many arbitrary functions that can be identified with the coefficients of the quasi-linear part of the equation. Moreover, in general, we conjecture that two scalar integrable evolutionary partial differential equations having the same quasi-linear part are Miura equivalent. This conjecture is also consistent with the tensorial behaviour of these coefficients under general Miura transformations.
authors.affiliation: Department of Mathematics and Statistics , University of Toledo, 2801 W. Bancroft St. , Toledo, OH 43606, USA.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Arsie
authors.affiliation: Dipartimento di Matematica e Applicazioni , Università di Milano-Bicocca , Via Roberto Cozzi 53, 20125 Milano, Italy.
authors.forename: Paolo
authors.initials: P
authors.lastname: Lorenzoni
authors.affiliation: Department of Mathematics and Information Sciences , University of Northumbria at Newcastle, Pandon Building, Camden St. , Newcastle upon Tyne NE2 1XE, UK.
authors.forename: Antonio
authors.initials: A
authors.lastname: Moro
keywords: conservation laws; integrability; normal forms