 of the soliton solutions.  ![image](Figure-0.eps){width="00cm"}  [**Figure 0.**]{} Profile of the amplitude of the dark soliton $U=|u_0|$ at $t=0$. a: $c=c_0=0.00$, b: $c=0.00$, c: $c=0.000$. The profile a is a black soliton