  The existence of a dispersion-managed soliton in two-dimensional nonlinear
Schr\"odinger equation with periodically varying dispersion has been explored.
The averaged equations for the soliton width and chirp are obtained which
successfully describe the long time evolution of the soliton. The slow dynamics
of the soliton around the fixed points for the width and chirp are investigated
and the corresponding frequencies are calculated. Analytical predictions are
confirmed by direct PDE and ODE simulations. Application to a Bose-Einstein
condensate in optical lattice is discussed. The existence of a
dispersion-managed matter-wave soliton in such system is shown.
