{"title":"杜布罗温法和户田链","authors":"V. Matveev, A. Smirnov","doi":"10.1090/spmj/1787","DOIUrl":null,"url":null,"abstract":"<p>A hierarchy of Lax pairs with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2 times 2\"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×<!-- × --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">2\\times 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrix coefficients is presented. The compatibility conditions for these pairs include the Toda chain equation, and other differential-difference integrable systems. Various kinds of finite gap solutions for such systems are constructed. Examples of simplest one- and two-phase solutions are given, together with the corresponding spectral curves.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":"19 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dubrovin method and the Toda chain\",\"authors\":\"V. Matveev, A. Smirnov\",\"doi\":\"10.1090/spmj/1787\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A hierarchy of Lax pairs with <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"2 times 2\\\"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×<!-- × --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">2\\\\times 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrix coefficients is presented. The compatibility conditions for these pairs include the Toda chain equation, and other differential-difference integrable systems. Various kinds of finite gap solutions for such systems are constructed. Examples of simplest one- and two-phase solutions are given, together with the corresponding spectral curves.</p>\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-01-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1787\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1787","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A hierarchy of Lax pairs with 2×22\times 2 matrix coefficients is presented. The compatibility conditions for these pairs include the Toda chain equation, and other differential-difference integrable systems. Various kinds of finite gap solutions for such systems are constructed. Examples of simplest one- and two-phase solutions are given, together with the corresponding spectral curves.
期刊介绍：
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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