Integrability, multi-soliton and rational solutions, and dynamical analysis for a relativistic Toda lattice system with one perturbation parameter

Meng-Li Qin,Xiao-Yong Wen,Cui-Lian Yuan

Figure 5. (Color online) Four-soliton elastic interaction structures via the solutions (55) with parameters ${\lambda }_{1}=\tfrac{1}{3},{\lambda }_{2}=\tfrac{5}{2},{\lambda }_{3}\,=3,{\lambda }_{4}=4,\alpha =\tfrac{3}{4},{C}_{11}=1,{C}_{12}=2,{C}_{21}=1,{C}_{22}=1,{C}_{31}=-1,{C}_{32}=1,{C}_{41}=1,{C}_{42}=2$. (a1) The component ${\tilde{a}}_{n}$. (a2) The component ${\tilde{b}}_{n}$. The propagation processes for $(b1)\ {\tilde{a}}_{n}$ and $(b2)\ | {\tilde{b}}_{n}| $ at t = − 6 (longdash line), t = 0 (dashdot line) and t = 6 (dot line).