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

► A theory of integrable dispersive deformations of 2+1 dimensional Hamiltonian systems of hydrodynamic type is developed. ► Triviality of first order deformations is established. ► Hamiltonians possessing nontrivial second order deformations are classified. ► Generic integrable Hamiltonians possess no nontrivial deformations.