Quasi-integrable deformations of the $SU(3)$ Affine Toda Theory

TL;DR

This paper explores deformations of the $SU(3)$ Affine Toda theory, revealing a phenomenon called quasi-integrability where conserved quantities are only asymptotically conserved during soliton scattering, supported by analytical and numerical evidence.

Contribution

It introduces the concept of quasi-integrability in deformed $SU(3)$ Affine Toda theories and analyzes the properties of solitons under these deformations.

Findings

Conserved charges are asymptotically conserved during soliton scattering.

Numerical simulations show solitons can repel or form quasi-bound states.

Solitons remain stable with minimal radiation in deformed models.

Abstract

We consider deformations of the $SU(3)$ Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only asymptotically, {\it i.e.} in the process of the scattering of two solitons these charges do vary in time, but they return, after the scattering, to the values they had prior to the scattering. This phenomenon, which we have called quasi-integrability, is related to special properties of the two-soliton solutions under space-time parity transformations. Some properties of the AT solitons are discussed, especially those involving interesting static multi-soliton solutions. We support our analytical studies with detailed numerical ones in which the time evolution has been simulated by the 4th order Runge-Kutta method. We find that for some perturbations the solitons repel and for the others they form a quasi-bound state. When we send solitons towards each other they can repel when they come close together with or without `flipping' the fields of the model. The solitons radiate very little and appear to be stable. These results support the ideas of quasi-integrability, {\it i.e.} that many effects of integrability also approximately hold for the deformed models.