Small and large data scattering for the dispersion-managed NLS
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| Název: | Small and large data scattering for the dispersion-managed NLS |
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| Autoři: | Kawakami, Jumpei, Murphy, Jason |
| Zdroj: | Discrete and Continuous Dynamical Systems. 47:256-285 |
| Publication Status: | Preprint |
| Informace o vydavateli: | American Institute of Mathematical Sciences (AIMS), 2026. |
| Rok vydání: | 2026 |
| Témata: | Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP) |
| Popis: | We prove several scattering results for dispersion-managed nonlinear Schrödinger equations. In particular, we establish small-data scattering for both `intercritical' and `mass-subcritical' powers by suitable modifications of the standard approach via Strichartz estimates. In addition, we prove scattering for arbitrary data in a weighted Sobolev space for intercritical powers by establishing a pseudoconformal energy estimate. We also rule out (unmodified) scattering for sufficiently low powers. Finally, we give some remarks concerning blowup for the focusing equation. 31 pages |
| Druh dokumentu: | Article |
| ISSN: | 1553-5231 1078-0947 |
| DOI: | 10.3934/dcds.2025118 |
| DOI: | 10.48550/arxiv.2407.11151 |
| Přístupová URL adresa: | http://arxiv.org/abs/2407.11151 |
| Rights: | arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....39fb210624b25fb1434d3a752330c163 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | We prove several scattering results for dispersion-managed nonlinear Schrödinger equations. In particular, we establish small-data scattering for both `intercritical' and `mass-subcritical' powers by suitable modifications of the standard approach via Strichartz estimates. In addition, we prove scattering for arbitrary data in a weighted Sobolev space for intercritical powers by establishing a pseudoconformal energy estimate. We also rule out (unmodified) scattering for sufficiently low powers. Finally, we give some remarks concerning blowup for the focusing equation.<br />31 pages |
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| ISSN: | 15535231 10780947 |
| DOI: | 10.3934/dcds.2025118 |