Discrete periodic solitons and dynamical analysis for an integrable coupled inhomogeneous lattice

In this article, a new integrable coupled inhomogeneous lattice is introduced and investigated, which can function as a useful system for the dynamics of broader nonlinear random lattices to describe the propagation behavior of water waves. First of all, an entirely novel integrable lattice hierarchy containing the mentioned system is constructed via the Tu scheme technique, and its Hamiltonian structures are given. Based on the obtained Lax pair, myriad conservation laws are derived, and the N-fold Darboux transformation concerning this system is subsequently built for the first time. Then, the multi-soliton solution and its graphical discussions are obtained, which exhibit novel periodic soliton and kinked periodic soliton structures and also demonstrate that the coefficients of the on-site external potential affect these wave structures. In particular, these novel periodic multi-soliton structures possessing oscillatory wave patterns differ from the straight-line behavior of propagation and interaction in semi-discrete coupled systems that are previously known. Lastly, numerical simulations are used to analyze the dynamics related to various kinds of sample one-soliton structures. Numerical results demonstrate that the propagation of these novel one-soliton solutions is less affected and stable by minor noises for a short time. What we obtained might help us interpret some wave propagation phenomena that occur in nonlinear media.