Stable two-dimensional dispersion-managed soliton

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.