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

Baron, H.E.; Zakrzewski, W.J.

Abstract

We investigate the validity of collective coordinate approximations to the scattering of two solitons in several classes of (1+1) dimensional field theory models. We consider models which are deformations of the sine-Gordon (SG) or the nonlinear Schr¨odinger (NLS) model which posses soliton solutions (which are topological (SG) or non-topological (NLS)). Our deformations preserve their topology (SG), but change their integrability properties, either completely or partially (models become ‘quasi-integrable’). As the collective coordinate approximation does not allow for the radiation of energy out of a system we look, in some detail, at how the approximation fares in models which are ‘quasi-integrable’ and therefore have asymptotically conserved charges (i.e. charges Q(t) for which Q(t →−∞) = Q(t →∞)). We find that our collective coordinate approximation, based on geodesic motion etc, works amazingly well in all cases where it is expected to work. This is true for the physical properties of the solitons and even for their quasi-conserved (or not) charges. The only time the approximation is not very reliable (and even then the qualitative features are reasonable, but some details are not reproduced well) involves the processes when the solitons come very close together (within one width of each other) during their scattering.

Citation

Baron, H., & Zakrzewski, W. (2016). Collective coordinate approximation to the scattering of solitons in modified NLS and sine-Gordon models. Journal of High Energy Physics, 2016(6), Article 185. https://doi.org/10.1007/jhep06%282016%29185

• Journal Article Type: Article
• Acceptance Date: Jun 20, 2016
• Online Publication Date: Jun 30, 2016
• Publication Date: Jun 30, 2016
• Deposit Date: Apr 1, 2019
• Publicly Available Date: Apr 2, 2019
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2016
• Issue: 6
• Article Number: 185
• DOI: https://doi.org/10.1007/jhep06%282016%29185
• Public URL: https://durham-repository.worktribe.com/output/1299623