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

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 Added by E. V. Ferapontov
 Publication date 2011
  fields Physics
and research's language is English




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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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