{"title":"大分级修正的户田等级体系及其扩展","authors":"Yi Yang , Wenjuan Rui , Jipeng Cheng","doi":"10.1016/j.physd.2024.134343","DOIUrl":null,"url":null,"abstract":"<div><p>Modified Toda hierarchy is just the two-component first modified KP hierarchy, which is related to 2D Toda hierarchy through Miura transformation and also has been widely used in discussing the B-Toda and C-Toda hierarchies. In this paper, we firstly construct <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math></span>-bigraded modified Toda hierarchy (BMTH) as a reduction of modified Toda hierarchy, and give corresponding Lie algebra interpretation. After that, we propose two kinds of extensions of <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math></span>-BMTH. One is extended by using logarithmic flows, while the other is <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>D extension, which is corresponding to the toroidal Lie algebra <span><math><msubsup><mrow><mi>sl</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>tor</mi></mrow></msubsup></math></span>. At last, the relation of these two kinds of extensions also is discussed.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bigraded modified Toda hierarchy and its extensions\",\"authors\":\"Yi Yang , Wenjuan Rui , Jipeng Cheng\",\"doi\":\"10.1016/j.physd.2024.134343\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Modified Toda hierarchy is just the two-component first modified KP hierarchy, which is related to 2D Toda hierarchy through Miura transformation and also has been widely used in discussing the B-Toda and C-Toda hierarchies. In this paper, we firstly construct <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math></span>-bigraded modified Toda hierarchy (BMTH) as a reduction of modified Toda hierarchy, and give corresponding Lie algebra interpretation. After that, we propose two kinds of extensions of <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math></span>-BMTH. One is extended by using logarithmic flows, while the other is <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>D extension, which is corresponding to the toroidal Lie algebra <span><math><msubsup><mrow><mi>sl</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>tor</mi></mrow></msubsup></math></span>. At last, the relation of these two kinds of extensions also is discussed.</p></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-08-29\",\"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/S016727892400294X\",\"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/S016727892400294X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Bigraded modified Toda hierarchy and its extensions
Modified Toda hierarchy is just the two-component first modified KP hierarchy, which is related to 2D Toda hierarchy through Miura transformation and also has been widely used in discussing the B-Toda and C-Toda hierarchies. In this paper, we firstly construct -bigraded modified Toda hierarchy (BMTH) as a reduction of modified Toda hierarchy, and give corresponding Lie algebra interpretation. After that, we propose two kinds of extensions of -BMTH. One is extended by using logarithmic flows, while the other is D extension, which is corresponding to the toroidal Lie algebra . At last, the relation of these two kinds of extensions also is discussed.
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