  We study the dynamics of two gray solitons in a Bose-Einstein condensate
confined by a toroidal trap with a tight confinement in the radial direction.
Gross-Pitaevskii simulations show that solitons can be long living objects
passing through many collisional processes. We have observed quite different
behaviors depending on the soliton velocity. Very slow solitons, obtained by
perturbing the stationary solitonic profile, move with a constant angular
velocity until they collide elastically and move in the opposite direction
without showing any sign of lowering their energy. In this case the density
notches are always well separated and the fronts are sharp and straight. Faster
solitons present vortices around the notches, which play a central role during
the collisions. We have found that in these processes the solitons lose energy,
as the outgoing velocity turns out to be larger than the incoming one. To study
the dynamics, we model the gray soliton state with a free parameter that is
related to the soliton velocity. We further analyze the energy, soliton
velocity and turning points in terms of such a free parameter, finding that the
main features are in accordance with the infinite one-dimensional system.
