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 3. (Color online) Head-on elastic interaction between two solitons via the solutions (54) with parameters ${\lambda }_{1}=\tfrac{1}{3},{\lambda }_{2}=3,\alpha ={C}_{11}={C}_{12}={C}_{21}=1,{C}_{22}=\tfrac{1}{2}$. (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 (longdash line), t = 0 (dashdot line) and t = 10 (dot line).