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arXiv · 2407.20277

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

Jian-Zhou Zhu
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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, called ``longons'', 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.

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Jian-Zhou Zhu. 2024-07-25. Travelling-wave, Quasi-periodic, and Longulent States of the Galerkin-regularized Hydrodynamic-type Systems. https://arxiv.org/abs/2407.20277

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