Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Order One and Two

TL;DR

This paper presents a comprehensive set of exact quasiperiodic solutions for various coupled discrete models in physics using Lame polynomials of orders one and two, revealing broader classes of solutions.

Contribution

It introduces new exact solutions for several coupled discrete models in physics using Lame polynomials, expanding the understanding of their solution space.

Findings

Exact quasiperiodic solutions for multiple coupled models

Solutions expressed in terms of Lame polynomials of order one and two

Most models also have broader classes of exact solutions

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 Lame 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 Schrodinger equation, (iv) coupled phi4 model, and (v) coupled phi6 model. Furthermore, we show that most of these coupled models in fact also possess an even broader class of exact solutions.