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

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

2011-08-22

arxiv.org/abs/1108.4365v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages

Scientific paper

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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