Figure 1

(a1), (b1) Overtaking elastic interactions of dark two-soliton solution \(\widetilde{u}_{n}\) in (43) with the parameters \(r_{1}=-1\), \(r_{2}=1\), \(\lambda_{1}=-2\), \(\lambda_{2}=-4\). (a2), (b2) Overtaking elastic interactions of bright two-soliton solution \(\widetilde{v}_{n}\) in (43) with the same parameters as in (a1), (b1). The interaction processes for (c1) \(\widetilde{u}_{n}\) and (c2) \(\widetilde{v}_{n}\) at \(t=-10\) (dash-dot line), \(t=0\) (dashed line), and \(t=10\) (solid line)