  We study a long wave-length asymptotics for the Gross-Pitaevskii equation
corresponding to perturbation of a constant state of modulus one. We exhibit
lower bounds on the first occurence of possible zeros (vortices) and compare
the solutions with the corresponding solutions to the linear wave equation or
variants. The results rely on the use of the Madelung transform, which yields
the hydrodynamical form of the Gross-Pitaevskii equation, as well as of an
augmented system.
