Small and large data scattering for the dispersion-managed NLS
We prove several scattering results for dispersion-managed nonlinear Schr\"odinger 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 additi...
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| creator | Kawakami, Jumpei Murphy, Jason |
| description | We prove several scattering results for dispersion-managed nonlinear
Schr\"odinger 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. |
| doi_str_mv | 10.48550/arxiv.2407.11151 |
| format | Article |
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Schr\"odinger 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.</description><identifier>DOI: 10.48550/arxiv.2407.11151</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2024-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2407.11151$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2407.11151$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kawakami, Jumpei</creatorcontrib><creatorcontrib>Murphy, Jason</creatorcontrib><title>Small and large data scattering for the dispersion-managed NLS</title><description>We prove several scattering results for dispersion-managed nonlinear
Schr\"odinger 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.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMjEw1zM0NDQ15GSwC85NzMlRSMxLUchJLEpPVUhJLElUKE5OLClJLcrMS1dIyy9SKMkAimcWF6QWFWfm5-nmJuYlpqemKPj5BPMwsKYl5hSn8kJpbgZ5N9cQZw9dsE3xBUWZuYlFlfEgG-PBNhoTVgEAQRA1aA</recordid><startdate>20240715</startdate><enddate>20240715</enddate><creator>Kawakami, Jumpei</creator><creator>Murphy, Jason</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240715</creationdate><title>Small and large data scattering for the dispersion-managed NLS</title><author>Kawakami, Jumpei ; Murphy, Jason</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2407_111513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Kawakami, Jumpei</creatorcontrib><creatorcontrib>Murphy, Jason</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kawakami, Jumpei</au><au>Murphy, Jason</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Small and large data scattering for the dispersion-managed NLS</atitle><date>2024-07-15</date><risdate>2024</risdate><abstract>We prove several scattering results for dispersion-managed nonlinear
Schr\"odinger 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.</abstract><doi>10.48550/arxiv.2407.11151</doi><oa>free_for_read</oa></addata></record> |
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| source | arXiv.org |
| subjects | Mathematics - Analysis of PDEs |
| title | Small and large data scattering for the dispersion-managed NLS |
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