A lattice hierarchy associated with RTL[formula omitted] system: Hamiltonian structures, discrete [formula omitted]-fold Darboux transformation, soliton elastic interactions and dynamics

Abstract

Starting from a 2 × 2 discrete matrix spectral problem, we construct an integrable lattice hierarchy associated with RTL+(α) system which is a one-parameter perturbation of the usual Toda lattice system describing the particle motion in a lattice. Based on the obtained RTL+(α) hierarchy, some integrable properties such as Hamiltonian structures, Liouville integrability and conservation laws are investigated. Furthermore, we establish the discrete N-fold Darboux transformation (DT) of RTL+(α) system. As applications of the obtained DT, multi-soliton solutions are derived on constant seed backgrounds, and discrete soliton propagation and elastic interaction structures are shown graphically and analyzed via asymptotic analysis. Numerical simulations are utilized to demonstrate the dynamical behaviors of such soliton solutions. Numerical results show that soliton evolutions are stable against a small noise. Results given in this paper might be helpful for understanding the propagation of nonlinear waves in soliton theory.