  By calculating the density response function we identify the excitation
spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus
spin-orbit coupling. We find that the velocity of sound along the direction of
spin-orbit coupling is deeply quenched and vanishes when one approaches the
second-order phase transition between the plane wave and the zero momentum
quantum phases. We also point out the emergence of a roton minimum in the
excitation spectrum for small values of the Raman coupling, providing the onset
of the transition to the stripe phase. Our findings point out the occurrence of
a strong anisotropy in the dynamic behavior of the gas. A hydrodynamic
description accounting for the collective oscillations in both uniform and
harmonically trapped gases is also derived.
