Stabilisation of spatially periodic states by non-Hermitian potentials

We uncover new families of stable periodic solutions by the introduction of non-Hermitian potentials in the universal complex Ginzburg–Landau equation. We perform a comprehensive analysis on the dynamics and stability of the system by determining and following these new solutions for a one-dimensional system, and demonstrate that the results hold for higher spatial dimensions and for the corresponding complex Ginzburg–Landau fractional order equation. We prove the robustness of the stabilisation within a broad range in parameter space. The universality of the CGLE allows extending these results to different actual systems described by other specific models. In particular, we provide results on the stabilisation for Vertical Cavity Surface Emitting Lasers.