Integrability of Differential-Difference Equations with Discrete Kinks

TL;DR

This paper investigates the integrability of certain discrete models approximating ^4 theory with traveling kinks, showing they exhibit some integrability features but are ultimately non-integrable.

Contribution

It applies multiple scale analysis to assess the integrability of models preserving discrete kink solutions, revealing partial integrability properties.

Findings

Models pass A_1 and A_2 integrability conditions

Models fail A_3 condition, indicating non-integrability

Partial integrability features identified through multiple scale test

Abstract

In this article we discuss a series of models introduced by Barashenkov, Oxtoby and Pelinovsky to describe some discrete approximations to the \phi^4 theory which preserve travelling kink solutions. We show, by applying the multiple scale test that they have some integrability properties as they pass the A_1 and A_2 conditions. However they are not integrable as they fail the A_3 conditions.