  We introduce spatiotemporal solitons of the two-dimensional complex
Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in
which asymmetry between space-time variables is included. The 2D CCQGLE is
solved by a powerful Fourier spectral method, i.e., a Fourier spatial
discretization and an explicit scheme for time differencing. Varying the
system's parameters, and using different initial conditions, numerical
simulations reveal 2D solitons in the form of stationary, pulsating and
exploding solitons which possess very distinctive properties. For certain
regions of parameters, we have also found stable coherent structures in the
form of spinning (vortex) solitons which exist as a result of a competition
between focusing nonlinearities and spreading while propagating through medium.
