Hamiltonian formulation for perfect fluid equations with the ℓ–conformal Galilei symmetry

Abstract

The Hamiltonian formulation for perfect fluid equations with the ℓ-conformal Galilei symmetry is proposed. For an arbitrary half-integer value of the parameter ℓ, the Hamilton and non-canonical Poisson brackets are found, in terms of which the original higher derivative equations of motion take the conventional Hamiltonian form. The full set of conserved charges is found and their algebra is established.