  The excitations of a two-dimensional (2D) Bose-Einstein condensate in the
presence of a soliton are studied by solving the Kadomtsev-Petviashvili
equation which is valid when the velocity of the soliton approaches the speed
of sound. The excitation spectrum is found to contain states which are
localized near the soliton and have a dispersion law similar to the one of the
stable branch of transverse oscillations of a 1D gray soliton in a 2D
condensate. By using the stabilization method we show that these localized
excitations behave as resonant states coupled to the continuum of free
excitations of the condensate.
