Domain Wall and Periodic Solutions of Coupled phi6 and Coupled phi6-phi4 Models

TL;DR

This paper derives higher order periodic solutions for coupled phi6 and phi6-phi4 models using Lame polynomials, revealing solutions unique to the coupled systems and covering different phase transition types.

Contribution

It presents novel exact solutions for coupled phi6 and phi6-phi4 models, including solutions not reducible to uncoupled cases, and covers various phase transition scenarios.

Findings

Higher order periodic solutions via Lame polynomials

Solutions unique to coupled systems, not uncoupled

Exact solutions for different phase transition types

Abstract

We obtain several higher order periodic solutions of a Coupled phi6 model in terms of Lame polynomials of order one and two. These solutions are unusual in the sense that while they are the solutions of the coupled problem, they are not the solutions of the uncoupled problem. We also obtain exact solutions of coupled phi6-phi4 models, both when the phi4 potential corresponds to a first order (asymmetric double well) or a second order (symmetric double well) transition.