  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.
