{"title":"Kadomtsev-Petviashvili方程耦合解的渐近性","authors":"Igor Anders","doi":"10.1016/S0764-4442(01)02070-5","DOIUrl":null,"url":null,"abstract":"<div><p>We determine a subset in <span><math><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup></math></span> and a measure on this set which allow to construct coupled non-localized solutions of the KP-I equation, which are connected by the change of variables (<em>x</em>,<em>t</em>)↦(−<em>x</em>,−<em>t</em>), and split into asymptotic solitons as <em>t</em>→∞ in the neighbourhood of the leading edge of the solutions. The solitons corresponding to each of the solutions have different amplitudes and lines of constant phase.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 891-896"},"PeriodicalIF":0.0000,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02070-5","citationCount":"1","resultStr":"{\"title\":\"Asymptotics of coupled solutions of the Kadomtsev–Petviashvili equation\",\"authors\":\"Igor Anders\",\"doi\":\"10.1016/S0764-4442(01)02070-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We determine a subset in <span><math><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup></math></span> and a measure on this set which allow to construct coupled non-localized solutions of the KP-I equation, which are connected by the change of variables (<em>x</em>,<em>t</em>)↦(−<em>x</em>,−<em>t</em>), and split into asymptotic solitons as <em>t</em>→∞ in the neighbourhood of the leading edge of the solutions. The solitons corresponding to each of the solutions have different amplitudes and lines of constant phase.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 9\",\"pages\":\"Pages 891-896\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02070-5\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201020705\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201020705","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Asymptotics of coupled solutions of the Kadomtsev–Petviashvili equation
We determine a subset in and a measure on this set which allow to construct coupled non-localized solutions of the KP-I equation, which are connected by the change of variables (x,t)↦(−x,−t), and split into asymptotic solitons as t→∞ in the neighbourhood of the leading edge of the solutions. The solitons corresponding to each of the solutions have different amplitudes and lines of constant phase.
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