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We investigate the validity of collective coordinate approaximations to thescattering of solitons in several classes of models in (1+1) dimensional fieldtheory models. We look at models which are deformations of the sine-Gordon (SG)or the nonlinear Schr\"odinger (NLS) model as they posses solitons which aretopological (SG) or non-topological (NLS). Our deformations preserve theirtopology (SG), but changes their integrability properties, either completely orpartially (models become `quasi-integrable').  As our collective coordinate approximation does not allow for the radiationof energy out the system we look also, in some detail, at how good thisapproximation is for models which are `quasi-integrable'. Our results are basedon the studies of the interactions and scatterings in two soliton systems.  Our results show that a well chosen approximation, based on geodesic motionetc, works amazingly well in all cases where it is expected to work. This istrue for the trajectories of the solitons and even for their quasi-conserved(or not) charges. The only time the approximation is not very reliable (andeven then the qualitative features are reasonable, but some details are notreproduced well) involves the processes when the solitons, during theirscattering, can come very close together (within one width of each other).

Collective coordinate approximation to the scattering of solitons in modified NLS and sine-Gordon models