  We classify the dispersive Poisson brackets with one dependent variable and
two independent variables, with leading order of hydrodynamic type, up to Miura
transformations. We show that, in contrast to the case of a single independent
variable for which a well known triviality result exists, the Miura equivalence
classes are parametrised by an infinite number of constants, which we call
numerical invariants of the brackets. We obtain explicit formulas for the first
few numerical invariants.
