Travelling-wave, Quasi-periodic, and Longulent States of the Galerkin-regularized Hydrodynamic-type Systems

Abstract: Travelling-wave, quasi-periodic and longulent'' states of the Galerkin-regularized systems preserving finite Fourier modes are exposed. The longulent states are characterized by solitonic structures, calledlongons'', accompanied by disordered components, which is associated to whiskered tori according to the \textit{a-posteriori} Kolmogorov-Arnold-Moser (KAM) theorem. On-torus invariants are introduced for constructing the KAM tori, towards a potential pseudo-integrability theory. Persistence of the longulent states with respect to certain dispersive and dissipative perturbations are also numerically indicated.