The fate of a gray soliton in a quenched Bose-Einstein condensate

We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the non-linearity parameter. The outcome of the quench is found to depend dramatically on the ratio $\eta$ of the final and initial values of the speed of sound. For integer $\eta$ the soliton splits into exactly $2\eta-1$ solitons. For non-integer $\eta$ the soliton decays into multiple solitons and Bogoliubov modes. The case of integer $\eta$ is analyzed in detail. The parameters of solitons in the out-state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for the similar quenches in any classical integrable system.