Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems
Exactly Solvable and Integrable Systems
2012-10-01 v3
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.
Cite
@article{arxiv.0807.2409,
title = {Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems},
author = {E. V. Ferapontov and A. Moro},
journal= {arXiv preprint arXiv:0807.2409},
year = {2012}
}
Comments
18 pages, section added