  Two applications of the Noether method for fluids and plasmas are presented
based on the Euler-Lagrange and Euler-Poincare variational principles, which
depend on whether the dynamical fields are to be varied independently or not,
respectively. The relativistic cold laser-plasma equations, describing the
interaction between an intense laser field with a cold relativistic electron
plasma, provide a useful set of equations amenable to both variational
formulations. The derivation of conservation laws by Noether method proceeds
from the Noether equation, whose form depends on the variational formulation
used. As expected, the expressions for the energy-momentum conservation laws
are identical in both variational formulations. The connection between the two
Lagrangian densities is shown to involve the mass conservation and Lin
constraints associated with the cold relativistic electron fluid.
