Solutions of several coupled discrete models in terms of Lamé polynomials of order one and two

Abstract

Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lamé polynomials of order one and two. Some of the models discussed are: (i) coupled Salerno model, (ii) coupled Ablowitz–Ladik model, (iii) coupled saturated discrete nonlinear Schrödinger equation, (iv) coupled ϕ 4 model and (v) coupled ϕ 6 model. Furthermore, we show that most of these coupled models in fact also possess an even broader class of exact solutions.