Figure 12

Collisions of four-soliton solutions \(\widetilde{u}_{n}\) and \(\widetilde{v}_{n}\) in (50) with \(N=2\) via the parameters \(r_{1}=\frac{1}{2}\), \(r_{2}=-\frac {1}{2}\), \(r_{3}=1\), \(r_{4}=-1\), \(\lambda_{1}=-3\), \(\lambda_{2}=-\frac{5}{2}\), \(\lambda_{3}=-2\), \(\lambda_{4}=-\frac{3}{2}\). (a) Exact solution; (b) Time evolution using exact solution as an initial condition; (c) Time evolution using exact solution perturbed by a 2% noise as the initial condition