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arXiv · 1108.4365

Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions

E. V. Ferapontov·V. S. Novikov·N. M. Stoilov
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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.

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E. V. Ferapontov, V. S. Novikov, N. M. Stoilov. 2011-08-22. Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions. https://doi.org/10.1016/j.physd.2011.12.004

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