Langmuir dark solitons in dense ultrarelativistic electron-positron gravito-plasma in pulsar magnetosphere

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.