{"title":"The extended versions of the noncommutative KP and mKP equations and Miura transformation","authors":"Muhammad Kashif, Li Chunxia, Cui Mengyuan","doi":"arxiv-2404.11391","DOIUrl":null,"url":null,"abstract":"Extended versions of the noncommutative(nc) KP equation and the nc mKP\nequation are constructed in a unified way, for which two types of\nquasideterminant solutions are also presented. In commutative setting, the\nquasideterminant solutions provide the known and unknown Wronskian and Grammian\nsolutions for the bilinear KP equation with self-consistent sources and the\nbilinear mKP equation with self-consistent sources, respectively. Miura\ntransformation is established for the extended nc KP and nc mKP equations.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Exactly Solvable and Integrable Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.11391","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Extended versions of the noncommutative(nc) KP equation and the nc mKP
equation are constructed in a unified way, for which two types of
quasideterminant solutions are also presented. In commutative setting, the
quasideterminant solutions provide the known and unknown Wronskian and Grammian
solutions for the bilinear KP equation with self-consistent sources and the
bilinear mKP equation with self-consistent sources, respectively. Miura
transformation is established for the extended nc KP and nc mKP equations.
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