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. 
O. Gamayun, Yu. V. Bezvershenko, V. Cheianov
cond-mat.quant-gas math-ph math.MP nlin.PS