Collective coordinate approximation to the scattering of solitons in modified NLS and sine-Gordon models
We use a collective coordinate approximation to model the scattering of two solitons in modified nonlinear Schr\"odinger and sine-Gordon systems. We find that the anomalies of the conservation laws of the charges as calculated using the collective coordinate approximation demonstrate the same dependence on the symmetry of the field configuration as that previously found analytically and using a full numerical simulation. This suggests that the collective coordinate approximation is a suitable method to investigate quasi-integrability in perturbed integrable models. We also discuss the general accuracy of this approximation by comparing our results with those of the full numerical simulations and find that the approximation is often remarkably accurate though less so when the models are a long way from the integrable case.