We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Department of Mathematical Sciences


Publication details for Professor Emeritus Wojtek Zakrzewski

Ferreira, L. A., Klimas, P. & Zakrzewski, Wojtek J. (2016). Quasi-integrable deformations of the SU(3) Affine Toda theory. Journal of High Energy Physics 2016(5): 65.

Author(s) from Durham


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, 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, i.e. that many effects of integrability also approximately hold for the deformed models.