.  ![image](Figure-0.eps){width="00cm"}  [**Figure 0.**]{} Amplitude-velocity relation for the dark soliton $A_d$ (solid line) and bright soliton $A_b$ (broken line) for $\rho=0$ and $\kappa=0$.  Figure 0 plots the dependence of the amplitudes $A=A_d$ and $A=A_b$ on the velocity $c=|c_0|$ for $\rho=0$ and $\kappa=0$.  ![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