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Updated: Apr 18, 2026

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
On integrable conservation laws
Alessandro Arsie1, Paolo Lorenzoni2, Antonio Moro3
1Department of Mathematics and Statistics , University of Toledo, 2801 W. Bancroft St. , Toledo, OH 43606, USA.
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.
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