Shielding of breathers for the focusing nonlinear Schrödinger equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908816906387456 |
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| author | Falqui, Gregorio Grava, Tamara Puntini, Christian |
| author_facet | Falqui, Gregorio Grava, Tamara Puntini, Christian |
| contents | We study a deterministic gas of breathers for the Focusing Nonlinear Schrödinger equation. The gas of breathers is obtained from a $N$-breather solution in the limit $N\to \infty$.\\ The limit is performed at the level of scattering data by letting the $N$-breather spectrum to fill uniformly a suitable compact domain of the complex plane in the limit $N\to\infty$. The corresponding norming constants are interpolated by a smooth function and scaled as $1/N$. For particular choices of the domain and the interpolating function, the gas of breathers behaves as finite breathers solution. This extends the shielding effect discovered in "M. Bertola, T. Grava, and G. Orsatti - Physical Review Letters, 130.12 (2023): 1" for a soliton gas also to a breather gas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shielding of breathers for the focusing nonlinear Schrödinger equation Falqui, Gregorio Grava, Tamara Puntini, Christian Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Pattern Formation and Solitons We study a deterministic gas of breathers for the Focusing Nonlinear Schrödinger equation. The gas of breathers is obtained from a $N$-breather solution in the limit $N\to \infty$.\\ The limit is performed at the level of scattering data by letting the $N$-breather spectrum to fill uniformly a suitable compact domain of the complex plane in the limit $N\to\infty$. The corresponding norming constants are interpolated by a smooth function and scaled as $1/N$. For particular choices of the domain and the interpolating function, the gas of breathers behaves as finite breathers solution. This extends the shielding effect discovered in "M. Bertola, T. Grava, and G. Orsatti - Physical Review Letters, 130.12 (2023): 1" for a soliton gas also to a breather gas. |
| title | Shielding of breathers for the focusing nonlinear Schrödinger equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2412.16696 |