{"title":"分散管理 NLS 的全局存在与有限时间爆炸二分法","authors":"Mi-Ran Choi , Younghun Hong , Young-Ran Lee","doi":"10.1016/j.na.2024.113696","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the Gabitov–Turitsyn equation or the dispersion managed nonlinear Schrödinger equation of a power-type nonlinearity <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>av</mi></mrow></msub><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>+</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mrow><mo>(</mo><mrow><msup><mrow><mrow><mo>|</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mi>u</mi></mrow><mo>)</mo></mrow><mi>d</mi><mi>r</mi><mo>=</mo><mn>0</mn></mrow></math></span></span></span>and prove the global existence versus finite time blowup dichotomy for the mass-supercritical cases, that is, <span><math><mrow><mi>p</mi><mo>></mo><mn>9</mn></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113696"},"PeriodicalIF":1.3000,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global existence versus finite time blowup dichotomy for the dispersion managed NLS\",\"authors\":\"Mi-Ran Choi , Younghun Hong , Young-Ran Lee\",\"doi\":\"10.1016/j.na.2024.113696\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We consider the Gabitov–Turitsyn equation or the dispersion managed nonlinear Schrödinger equation of a power-type nonlinearity <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>av</mi></mrow></msub><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>+</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mrow><mo>(</mo><mrow><msup><mrow><mrow><mo>|</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mi>u</mi></mrow><mo>)</mo></mrow><mi>d</mi><mi>r</mi><mo>=</mo><mn>0</mn></mrow></math></span></span></span>and prove the global existence versus finite time blowup dichotomy for the mass-supercritical cases, that is, <span><math><mrow><mi>p</mi><mo>></mo><mn>9</mn></mrow></math></span>.</div></div>\",\"PeriodicalId\":49749,\"journal\":{\"name\":\"Nonlinear Analysis-Theory Methods & Applications\",\"volume\":\"251 \",\"pages\":\"Article 113696\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Theory Methods & Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0362546X24002153\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24002153","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Global existence versus finite time blowup dichotomy for the dispersion managed NLS
We consider the Gabitov–Turitsyn equation or the dispersion managed nonlinear Schrödinger equation of a power-type nonlinearity and prove the global existence versus finite time blowup dichotomy for the mass-supercritical cases, that is, .
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Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.
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