Numerical evidence for singularity formation in defocusing fractional NLS in one space dimension
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929708766068736 |
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| author | Klein, Christian Sparber, Christof |
| author_facet | Klein, Christian Sparber, Christof |
| contents | We consider nonlinear dispersive equations of Schrödinger-type involving fractional powers $0<s\le 1$ of the Laplacian and a defocusing power-law nonlinearity. We conduct numerical simulations in the case of small, energy supercritical $s$ and provide evidence for a novel type of highly oscillatory singularity within the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18047 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical evidence for singularity formation in defocusing fractional NLS in one space dimension Klein, Christian Sparber, Christof Analysis of PDEs We consider nonlinear dispersive equations of Schrödinger-type involving fractional powers $0<s\le 1$ of the Laplacian and a defocusing power-law nonlinearity. We conduct numerical simulations in the case of small, energy supercritical $s$ and provide evidence for a novel type of highly oscillatory singularity within the solution. |
| title | Numerical evidence for singularity formation in defocusing fractional NLS in one space dimension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.18047 |