Higher Order Periodic Solutions of Coupled phi4 Models

TL;DR

This paper derives higher order exact periodic solutions for various coupled phi4 models using Lame polynomials, revealing solutions unique to the coupled systems that do not exist in uncoupled cases.

Contribution

It introduces novel higher order periodic solutions for coupled phi4 models expressed through Lame polynomials, expanding the understanding of these systems.

Findings

Solutions expressed in terms of Lame polynomials of order two

Existence of solutions not reducible to uncoupled models

Hyperbolic solutions obtained in specific limits

Abstract

We obtain several higher order exact periodic solutions of (i) a coupled symmetric phi4 model in an external field, (ii) an asymmetric coupled phi4 model, (iii) an asymmetric-symmetric coupled phi4 model, in terms of Lame polynomials of order two and obtain the corresponding hyperbolic solutions in the appropriate limit. These solutions are unusual in the sense that while they are the solutions of the coupled problems, they are not the solutions of the corresponding uncoupled problems.