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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20277 |
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| _version_ | 1866912218178650112 |
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| author | Zhu, Jian-Zhou |
| author_facet | Zhu, Jian-Zhou |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Travelling-wave, Quasi-periodic, and Longulent States of the Galerkin-regularized Hydrodynamic-type Systems Zhu, Jian-Zhou Pattern Formation and Solitons High Energy Physics - Phenomenology 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. |
| title | Travelling-wave, Quasi-periodic, and Longulent States of the Galerkin-regularized Hydrodynamic-type Systems |
| topic | Pattern Formation and Solitons High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2407.20277 |