Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions
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.
- Publication:
-
Physica D Nonlinear Phenomena
- Pub Date:
- December 2012
- DOI:
- 10.1016/j.physd.2011.12.004
- arXiv:
- arXiv:1108.4365
- Bibcode:
- 2012PhyD..241.2138F
- Keywords:
-
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- 35L40;
- 37K05;
- 37K10;
- 37K55
- E-Print:
- 16 pages