  We study the collisional dynamics of multiple dark solitons in a
Bose-Einstein condensate confined by a toroidal trap. We assume a tight enough
confinement in the radial direction to prevent possible dissipative effects due
to the presence of solitonic vortices. Analytical expressions for the initial
order parameters with imprinted phases are utilized to generate different
initial arrays of solitons, for which the time-dependent Gross-Pitaevskii
equation is numerically solved. Given that the soliton velocity is conserved
due to the lack of dissipation, we are able to apply a simple quasiparticle
description of the soliton dynamics. In fact, the trajectory equations are
written in terms of the velocities and the angular shifts produced at each
collision, in analogy to the infinite one-dimensional system. To calculate the
angular shifts, we directly extract them from the trajectories given by the
Gross-Pitaevskii simulations and, on the other hand, we show that accurate
values can be analytically obtained by adapting a formula valid for the
infinite one-dimensional system that involves the healing length, which in our
inhomogeneous system must be evaluated in terms of the sound velocity along the
azimuthal direction. We further show that very good estimates of such a sound
velocity can be directly determined by using the ground state density profile
and the values of the imprinted phases. We discuss the possible implementation
of the system here proposed using the current experimental techniques.

Quantum Gases