Dispersive deformations of hydrodynamic reductions of (2 + 1)D dispersionless integrable systems

Ferapontov, Eugene and Moro, Antonio (2008) Dispersive deformations of hydrodynamic reductions of (2 + 1)D dispersionless integrable systems. Journal of Physics A: Mathematical and Theoretical, 42 (3). 035211. ISSN 1751-8113

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Official URL: http://dx.doi.org/10.1088/1751-8113/42/3/035211

Abstract

We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2 + 1 dimensions, such as the dispersionless Kadomtsev–Petviashvili (dKP) and dispersionless Toda lattice (dTl) equations, can be deformed into reductions of the corresponding dispersive counterparts. Modulo the Miura group, such deformations are unique. The requirement that any hydrodynamic reduction possesses a deformation of this kind imposes strong constraints on the structure of dispersive terms, suggesting an alternative approach to the integrability in 2 + 1 dimensions.

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Ellen Cole
Date Deposited: 12 Jul 2013 10:28
Last Modified: 10 Aug 2015 11:30
URI: http://nrl.northumbria.ac.uk/id/eprint/13211

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