{"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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