  We study, analytically and numerically, the dynamical behavior of the
solutions of the complex Ginzburg-Landau equation with diffraction but without
diffusion, which governs the spatial evolution of the field in an active
nonlinear laser cavity. Accordingly, the solutions are subject to periodic
boundary conditions. The analysis reveals regions of stable stationary
solutions in the model&#8217;s parameter space, and a wide range of oscillatory
and chaotic behaviors. Close to the first bifurcation destabilizing the
spatially uniform solution, a stationary single-humped solution is found in an
asymptotic analytical form, which turns out to be in very good agreement with
the numerical results. Simulations reveal a series of stable stationary
multi-humped solutions
