Constructing Longulence in the Galerkin-Regularized Nonlinear Schrödinger and Complex Ginzburg-Landau Systems

(Quasi-)periodic solutions are constructed analytically for Galerkin-regularized or Fourier truncated nonlinear Schrödinger (GrNLS) systems and numerically for those of complex Ginzburg-Landau (GrCGL). Compared to the simultaneous results of other Galerkin-regularized hydrodynamics-type systems, new GrNLS features include the existence of nontrivial monochromatic solutions or condensates (independent of the truncation) and of quasi-periodic tori with and without additional on-torus invariants. Numerical tests find that instability leads such solutions to nontrivial longulent states with remarkable solitonic longons admist disordered weaker components, corresponding to presumably whiskered tori. The possibility of nontrivial GrCGL longulent states is also discussed for motivation.