Stable localized pulses and zigzag stripes in a two-dimensional diffractive–diffusive Ginzburg–Landau equation

We introduce a model of a two-dimensional (2D) optical waveguide with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. In the general case, temporal dispersion is also included, although it is not necessary. The model provides for description of a nonlinear planar waveguide incorporated into a closed optical cavity. It takes the form of a 2D cubic–quintic Ginzburg–Landau equation with an anisotropy of a novel type: the equation is diffractive in one direction, and diffusive in the other. By means of systematic simulations, we demonstrate that the model gives rise to stable fully localized 2D pulses, which are spatiotemporal “light bullets”, existing due to the simultaneous balances between diffraction, dispersion, and Kerr nonlinearity, and between linear and quintic losses and cubic gain. A stability region of the 2D pulses is identified in the system’s parameter space. Besides that, we also find that the model generates 1D patterns in the form of simple localized stripes, which may be stable, or may exhibit an instability transforming them into oblique stripes with zigzags. The straight and oblique stripes may stably coexist with the 2D pulse, but not with each other.