Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions
Exactly Solvable and Integrable Systems
2015-05-30 v1 Mathematical Physics
math.MP
Abstract
We develop a theory of integrable dispersive deformations of 2+1 dimensional Hamiltonian systems of hydrodynamic type following the scheme proposed by Dubrovin and his collaborators in 1+1 dimensions. Our results show that the multi-dimensional situation is far more rigid, and generic Hamiltonians are not deformable. As an illustration we discuss a particular class of two-component Hamiltonian systems, establishing the triviality of first order deformations and classifying Hamiltonians possessing nontrivial deformations of the second order.
Keywords
Cite
@article{arxiv.1108.4365,
title = {Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions},
author = {E. V. Ferapontov and V. S. Novikov and N. M. Stoilov},
journal= {arXiv preprint arXiv:1108.4365},
year = {2015}
}
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16 pages