Ginzburg-Landau Equations with Cross-Phase Modulation

Below are solutions to a system of Ginzburg-Laundau equations where each wavefunction interacts with one another via an asymmetric cross-phase modulation parameter, leading to a separation of intensities. What is plotted is the intensity (complex modulus) of each wavefunction on the surface of the manifold (either a 2D plane, a sphere, or a torus). See and for details about the system in flat space.