Incoherent matter-wave solitons
  The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a surrounding thermal cloud and by condensate depletion during its evolution. We analyze these aspects of BEC soliton dynamics, using time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The condensate is initially prepared within a harmonic trap at finite temperature, and solitonic behavior is studied by subsequently propagating the TDHFB equations without confinement. Numerical results demonstrate the collapse of the BEC via collisional emission of atom pairs into the thermal cloud, resulting in splitting of the initial density into two solitonic structures with opposite momentum. Each one of these solitary matter waves is a mixture of condensed and noncondensed particles, constituting an analog of optical random-phase solitons. 
H. Buljan, M. Segev, and A. Vardi