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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2412.21142 |
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| _version_ | 1866929741126172672 |
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| author | Zhu, Jian-Zhou |
| author_facet | Zhu, Jian-Zhou |
| contents | (Quasi-)periodic solutions are constructed analytically for Galerkin-regularized or truncated nonlinear Schrödinger (GrNLS) systems preserving finite Fourier freedoms. GrNLS admits travelling-wave or multi-phase solutions, including monochromatic solutions independent of the truncation and quasi-periodic ones with or without additional on-torus invariants. Numerical tests show that instability leads such solutions to nontrivial longulent states with remarkable solitonic structures (called ``longons'') admist disordered weaker components, corresponding to presumably whiskered tori. In the strong-coupling limit (e.g., the self-phase modulation equation in optics), neutral stability holds for the condensates, without the modulational instability, but not generally for other multi-phase (quasi-)periodic solutions from some of which the longulent state developed is also adressed. The possibility of nontrivial Galerkin-regularized complex Ginzburg-Landau longulent states is also discussed for motivation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructing longulence in the Galerkin-regularized nonlinear Schrödinger and complex Ginzburg-Landau systems Zhu, Jian-Zhou Pattern Formation and Solitons (Quasi-)periodic solutions are constructed analytically for Galerkin-regularized or truncated nonlinear Schrödinger (GrNLS) systems preserving finite Fourier freedoms. GrNLS admits travelling-wave or multi-phase solutions, including monochromatic solutions independent of the truncation and quasi-periodic ones with or without additional on-torus invariants. Numerical tests show that instability leads such solutions to nontrivial longulent states with remarkable solitonic structures (called ``longons'') admist disordered weaker components, corresponding to presumably whiskered tori. In the strong-coupling limit (e.g., the self-phase modulation equation in optics), neutral stability holds for the condensates, without the modulational instability, but not generally for other multi-phase (quasi-)periodic solutions from some of which the longulent state developed is also adressed. The possibility of nontrivial Galerkin-regularized complex Ginzburg-Landau longulent states is also discussed for motivation. |
| title | Constructing longulence in the Galerkin-regularized nonlinear Schrödinger and complex Ginzburg-Landau systems |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2412.21142 |