On symmetry of traveling solitary waves for dispersion generalized NLS
| Autor: | Bugiera, Lars, Lenzmann, Enno, Schikorra, Armin, Sok, Jérémy |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1361-6544/ab74b2 |
| Popis: | We consider dispersion generalized nonlinear Schr\"odinger equations (NLS) of the form $i \partial_t u = P(D) u - |u|^{2 \sigma} u$, where $P(D)$ denotes a (pseudo)-differential operator of arbitrary order. As a main result, we prove symmetry results for traveling solitary waves in the case of powers $\sigma \in \mathbb{N}$. The arguments are based on Steiner type rearrangements in Fourier space. Our results apply to a broad class of NLS-type equations such as fourth-order (biharmonic) NLS, fractional NLS, square-root Klein-Gordon and half-wave equations. Comment: 17 pages. Any comments are welcome! |
| Databáze: | arXiv |
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