Variational analysis of soliton scattering by external potentials

Dynamics of the width and center-of-mass position of a matter wave soliton subject to interaction with arbitrary external potential is analyzed using the collective coordinates approach. It is shown that approximation of the trial function and external potential only in the interaction region of the spatial domain is sufficient for adequate description of the soliton scattering process. The validity of the developed approach is illustrated for the Gaussian and Pöschl-Teller potentials.