Some properties of deformed Sine Gordon models

TL;DR

This paper investigates properties of deformed Sine Gordon models, focusing on the existence and stability of breather solutions, and finds that true breathers likely do not exist, but long-lived quasi-breathers can occur in certain cases.

Contribution

It provides the first numerical analysis of breather solutions in deformed Sine Gordon models, revealing the existence of quasi-breathers and their stability properties.

Findings

Breathers probably do not exist in these models.

Some models exhibit long-lived quasi-breather solutions.

Results are consistent across different numerical discretizations.

Abstract

We study some properties of the deformed Sine Gordon models. These models, presented by Bazeia et al, are natural generalisations of the Sine Gordon models in (1+1) dimensions. There are two classes of them, each dependent on a parameter n. For special values of this parameter the models reduce to the Sine Gordon one; for other values of n they can be considered as generalisations of this model. The models are topological and possess one kink solutions. Here we investigate the existence of other solutions of these models - such as breathers. The work is numerical and we find that the breathers, as such, probably do not exist. However, we show that some of these models, namely, the n = 1 of the first class possess breather-like solutions which are quasi-stable; ie these quasi-breathers exist for long periods of time (thousands of periods of oscillations). These results are found to be independent of the discretisation used in the numerical part of our work.