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

Table 1. Main mathematical features of rational solutions an and bn of order j.

j HPN(an) HPD(an) HPN(bn) HPD(bn) Background(an) Background(bn) 1 2 2 0 2 1 0 2 12 12 10 12 1 0 3 30 30 28 30 1 0 ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ j 2j(2j − 1) 2j(2j − 1) 2j(2j − 1) − 2 2j(2j − 1) 1 0