Asymptotic interaction between solitons in the Nielsen - Olesen model

Abstract

The objective of this paper was to find the interaction between two vortex solitons in the Nielsen – Olensen model, these solitons are the asymptotic solutions in said model, in order to calculate this interaction it was assumed that these solitons are quasi-static and that they are very far between if and with the help of the momentum energy tensor, this interaction could be found in the z direction in a plane that symmetrically divides these two solitons, which presents two cases since there are two possible asymptotic solutions for the field function according to the coefficient β, the possible cases are for β < 4 and β > 4, in each of the cases interaction is found that depends on exponential functions, the distance between these solitons and the parameters found at the time of calculating said asymptotic solution that are constants {1, −1}. Furthermore, this force is similar to the force experienced by two turns with current that are very far from each other.