Breathing-soliton and singular rogue wave solutions for a discrete nonlocal coupled Ablowitz–Ladik equation of reverse-space type

Abstract

In this letter, inspired by the idea of Ablowitz and Musslimani, we propose and investigate a discrete nonlocal reverse-space coupled Ablowitz–Ladik equation. Based on its Lax pair, we construct discrete nonlocal version of the generalized (m,N−m)-fold Darboux transformation for this system. Using the resulting Darboux transformation, we can obtain its different types of exact solutions including breathing-soliton and singular rogue wave solutions from vanishing and plane wave backgrounds. Breathing-soliton propagation and interaction features are investigated through asymptotic analysis. The wave structures of these singular rogue wave solutions are discussed and shown graphically. It is clearly shown that these solutions have new properties which differ from ones of the local coupled Ablowitz–Ladik equation.