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

TL;DR

This paper develops a Hamiltonian framework for perfect fluid equations exhibiting l-conformal Galilei symmetry, including conserved charges and their algebra, for arbitrary half-integer l values.

Contribution

It introduces a Hamiltonian formulation for these fluid equations with symmetry, deriving brackets, conserved charges, and algebraic structure for arbitrary half-integer l.

Findings

Hamilton and non-canonical Poisson brackets derived

Higher derivative equations expressed in Hamiltonian form

Complete set of conserved charges and their algebra established

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.