On $$\varvec{\mathcal {PT}}$$-symmetric semi-discrete coupled integrable dispersionless system

Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type*

“…However, it is easy to find that most research results of nonlocal equations are the study of continuous nonlocal integrable equations, while the revelent research of discrete NLEs is not sufficient. [9,[33][34][35][36][37] Especially, the study of nonlocal discrete equations is not systematic, [38][39][40][41] so focusing on discrete nonlocal NLEs motivates us.…”

“…Some methods for solving local equations have been extended to nonlocal equations such as the inverse scattering transform method, [15,24,30] Hirota's bilinear method, [25,26,31,32,[42][43][44] the function expansion method, [27] the Riemann-Hilbert method, [28] and the DT method. [9,12,16,29,33,[35][36][37][38][39][40][41][45][46][47][48][49][50][51] Among them, DT is a simple algebraic technique to generate a family of infinite nontrivial solutions of a linear equation from a known trivial solution which is widely used in soliton theory. [9,45,46] It needs to be noted that the N-fold DT technique is a very effective method to derive N-soliton solutions compared to iterative DT because there is no iterative process.…”