  Nonlinear propagation of electrostatic modes in ultrarelativistic dense
elelectron-positron gravito-plasma at the polar cap region of pulsar
magnetosphere is considered. A nonlinear Schr\"{o}dinger equation is obtained
from the reductive perturbation method which predicts the existence of Langmuir
dark solitons. Relevance of the propagating dark solitons to the pulsar radio
emission is discussed.
