Some comments on quasi-integrability

In this paper we present our preliminary results which suggest that some field theory models are ‘almost’ integrable; i.e. they possess a large number of ‘almost’ conserved quantities. First we demonstrate this, in some detail, on a class of models which generalise sine-Gordon model in (1+1) dimensions. Then, we point out that many field configurations of these models look like those of the integrable systems and others are very close to being integrable. Finally we attempt to quantify these claims looking in particular, both analytically and numerically, at some long lived field configurations which resemble breathers.