$CP^2$ soliton scattering: The collective coordinate approximation

TL;DR

This paper analyzes soliton scattering in the $CP^2$ model using the collective coordinate approximation, revealing how a generalized Hopf term influences scattering angles through analytical solutions.

Contribution

It introduces an ansatz for the collective coordinate approximation in the $CP^2$ model with a Hopf term and derives analytical equations of motion for soliton scattering.

Findings

The generalized Hopf term alters the scattering angle from 90°.

Analytical solutions describe soliton interactions at different separations.

The ansatz accurately parameterizes numerical solutions in previous studies.

Abstract

The $CP^2$ model, with and without a generalized Hopf term, is studied using the collective coordinate approximation. In the spirit of this approximation, an ansatz is given which in previous numerical studies was seen to give a good parameterization of the numerical solution. The equations of motion for the collective coordinates are then solved analytically, for solitons close together and for solitons far apart. The solutions show how the generalized Hopf term changes the scattering angle which in its absence is $90^{\circ}$.