Multiphonon decay of solitons in Bose-Einstein condensates

The stability of the Jones-Roberts (JR) solitary waves in Bose-Einstein condensates with respect to quantum decay into several phonons is investigated. The conservation laws permits such a decay for the upper branch of JP dispersion curve and for the part of lower branch which lies above the sound line. The minimal number of phonons in which an excitation with given energy and momentum can decay is estimated. This number depends of the gas parameter of the fluid.