The concept of quasi-integrability

Abstract

The development of exact methods to study field theories is of crucial importance for the understanding of non-linear and non-perturbative (strong coupling) phenomena in Physics. Solitons are exact solutions of the so-called integrable field theories that possess an infinite number of conservation laws, and so are good candidates to lead to such exact methods. Unfortunately not many theories which describe real physical phenomena are within that class of integrable theories. It was recently discovered by Profs. Wojtek J. Zakrzewski and Luiz A. Ferreira that many theories which are not integrable present solutions that behave very similarly to solitons, i.e. such soliton like solution scatter through each other without distorting them very much. It was shown, in the context of deformations of the sine-Gordon model and other integrable theories, that such quasi-integrable theories possess and infinite number of charges that are asymptotically conserved. By that one means that during the scattering of two soliton like solutions such charges do vary in time (and quite a lot sometimes) but they all return in the remote future (after the scattering) to the values they had in the remote past (before the scattering). Since in a scattering process what matters are the asymptotic states, such theories are effectively integrable, and that is why they were named quasi-integrable. Such discovery opens up the way to the development of new methods to study theories of physical interest, with a large potential of applications, and that is the objective of the present project. (AU)