{"title":"半离散布辛斯克方程的黎曼 Theta 函数解","authors":"Yaru Xu , Xianguo Geng , Yunyun Zhai","doi":"10.1016/j.physd.2024.134398","DOIUrl":null,"url":null,"abstract":"<div><div>The hierarchy of the semi-discrete Boussinesq equations associated with a discrete 4 × 4 matrix spectral problem has been derived by means of the zero-curvature and the Lenard recursion equations. The tetragonal curve is introduced by resorting to the characteristic polynomial of the Lax matrix for the semi-discrete Boussinesq hierarchy, upon which the Baker-Akhiezer functions, meromorphic functions, Abel differentials, and Riemann theta functions are constructed. Finally, we derive the Riemann theta function solutions to the semi-discrete Boussinesq hierarchy.</div></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Riemann theta function solutions to the semi-discrete Boussinesq equations\",\"authors\":\"Yaru Xu , Xianguo Geng , Yunyun Zhai\",\"doi\":\"10.1016/j.physd.2024.134398\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The hierarchy of the semi-discrete Boussinesq equations associated with a discrete 4 × 4 matrix spectral problem has been derived by means of the zero-curvature and the Lenard recursion equations. The tetragonal curve is introduced by resorting to the characteristic polynomial of the Lax matrix for the semi-discrete Boussinesq hierarchy, upon which the Baker-Akhiezer functions, meromorphic functions, Abel differentials, and Riemann theta functions are constructed. Finally, we derive the Riemann theta function solutions to the semi-discrete Boussinesq hierarchy.</div></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167278924003488\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003488","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Riemann theta function solutions to the semi-discrete Boussinesq equations
The hierarchy of the semi-discrete Boussinesq equations associated with a discrete 4 × 4 matrix spectral problem has been derived by means of the zero-curvature and the Lenard recursion equations. The tetragonal curve is introduced by resorting to the characteristic polynomial of the Lax matrix for the semi-discrete Boussinesq hierarchy, upon which the Baker-Akhiezer functions, meromorphic functions, Abel differentials, and Riemann theta functions are constructed. Finally, we derive the Riemann theta function solutions to the semi-discrete Boussinesq hierarchy.
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