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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2403.12336 |
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| _version_ | 1866915274320510976 |
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| author | Moutinho, Abdon |
| author_facet | Moutinho, Abdon |
| contents | We study the global dynamics of the collision of two solitons having the same mass for one-dimensional Nonlinear Schrödinger models with multi-power nonlinearity. For any natural number k, it is verified that if the incoming speed v between the two solitary waves is small enough, then, after the collision, the two solitons will move away with an outcoming speed v_{f}=v+O(v^{k}) and the remainder of the solution will also have energy and weighted norms of order O(v^{k}). This is applied to the one-dimensional models with polynomial odd nonlinearity having a stable soliton such as the cubic NLS and the cubic-quintic NLS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Collision of two solitons for $1d$ Nonlinear Schrodinger Equation with the same mass Moutinho, Abdon Analysis of PDEs Mathematical Physics Classical Analysis and ODEs 35B35, 35B24, 35C11, 35C08 We study the global dynamics of the collision of two solitons having the same mass for one-dimensional Nonlinear Schrödinger models with multi-power nonlinearity. For any natural number k, it is verified that if the incoming speed v between the two solitary waves is small enough, then, after the collision, the two solitons will move away with an outcoming speed v_{f}=v+O(v^{k}) and the remainder of the solution will also have energy and weighted norms of order O(v^{k}). This is applied to the one-dimensional models with polynomial odd nonlinearity having a stable soliton such as the cubic NLS and the cubic-quintic NLS. |
| title | Collision of two solitons for $1d$ Nonlinear Schrodinger Equation with the same mass |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs 35B35, 35B24, 35C11, 35C08 |
| url | https://arxiv.org/abs/2403.12336 |