Soliton scattering: the collective coordinate approximation

Abstract

The 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 for the head-on collision of two solitons. 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 .