{"title":"多分量半离散短脉冲方程的准格拉米亚环路动力学","authors":"A. Inam, M. ul Hassan","doi":"10.1134/S0040577924090083","DOIUrl":null,"url":null,"abstract":"<p> A semidiscrete short-pulse equation (sdSPE) is presented via a proposed Lax pair. A multicomponent sdSPE is derived using <span>\\(2^M\\times 2^M\\)</span> Lax matrices. The standard binary Darboux transformation (SBDT) is employed by constructing the Darboux matrices from particular eigenvector solutions of the generalized Lax pair not only in the direct space but also in its adjoint space. Explicit expressions of the first- and second-order nontrivial quasi-Grammian loop solutions of the multicomponent sdSPE are computed, by iterating its SBDT. It is also shown that quasi-Grammian loop solutions reduce to the elementary loop solutions by applying reduction of spectral parameters. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 3","pages":"1530 - 1555"},"PeriodicalIF":1.0000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-Grammian loop dynamics of a multicomponent semidiscrete short pulse equation\",\"authors\":\"A. Inam, M. ul Hassan\",\"doi\":\"10.1134/S0040577924090083\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> A semidiscrete short-pulse equation (sdSPE) is presented via a proposed Lax pair. A multicomponent sdSPE is derived using <span>\\\\(2^M\\\\times 2^M\\\\)</span> Lax matrices. The standard binary Darboux transformation (SBDT) is employed by constructing the Darboux matrices from particular eigenvector solutions of the generalized Lax pair not only in the direct space but also in its adjoint space. Explicit expressions of the first- and second-order nontrivial quasi-Grammian loop solutions of the multicomponent sdSPE are computed, by iterating its SBDT. It is also shown that quasi-Grammian loop solutions reduce to the elementary loop solutions by applying reduction of spectral parameters. </p>\",\"PeriodicalId\":797,\"journal\":{\"name\":\"Theoretical and Mathematical Physics\",\"volume\":\"220 3\",\"pages\":\"1530 - 1555\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0040577924090083\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S0040577924090083","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Quasi-Grammian loop dynamics of a multicomponent semidiscrete short pulse equation
A semidiscrete short-pulse equation (sdSPE) is presented via a proposed Lax pair. A multicomponent sdSPE is derived using \(2^M\times 2^M\) Lax matrices. The standard binary Darboux transformation (SBDT) is employed by constructing the Darboux matrices from particular eigenvector solutions of the generalized Lax pair not only in the direct space but also in its adjoint space. Explicit expressions of the first- and second-order nontrivial quasi-Grammian loop solutions of the multicomponent sdSPE are computed, by iterating its SBDT. It is also shown that quasi-Grammian loop solutions reduce to the elementary loop solutions by applying reduction of spectral parameters.
期刊介绍:
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.