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 2. (Color online) One-soliton solutions with parameters ${\lambda }_{1}=\tfrac{3}{5},{\lambda }_{2}=2,\alpha =\tfrac{8}{15},{C}_{11}=1,{C}_{12}=\tfrac{1}{2},{C}_{21}=1,{C}_{22}=2$. (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 = −10 (long-dash line), t = 0 (dash-dot line) and t = 10 (dot line).