Numerical and analytical tests of quasi-integrability in modified Sine-Gordon models

TL;DR

This paper investigates quasi-integrability in modified Sine-Gordon models by analyzing soliton interactions and breather dynamics, showing that certain symmetries influence conservation law anomalies.

Contribution

It introduces a symmetry-based criterion for quasi-integrability and tests it through numerical and analytical methods in modified Sine-Gordon models.

Findings

Numerical scattering results support the symmetry condition.

Breather-like structures exhibit behavior consistent with quasi-integrability.

Symmetry of field configurations affects conservation law anomalies.

Abstract

Following our attempts to define quasi-integrability in which we related this concept to a particular symmetry of the two-soliton function we check this condition in three classes of modified Sine-Gordon models in (1+1) dimensions. We find that the numerical results seen in various scatterings of two solitons and in the time evolution of breather-like structures support our ideas about the symmetry of the field configurations and its effects on the anomalies of the conservation laws of the charges.