{"title":"A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions","authors":"T. Valchev","doi":"arxiv-2403.18165","DOIUrl":null,"url":null,"abstract":"We consider a matrix nonlinear partial differential equation that generalizes\nHeisenberg ferromagnet equation. This generalized Heisenberg ferromagnet\nequation is completely integrable with a linear bundle Lax pair related to the\npseudo-unitary algebra. This allows us to explicitly derive particular\nsolutions by using dressing technique. We shall discuss two classes of\nsolutions over constant background: soliton-like solutions and quasi-rational\nsolutions. Both classes have their analogues in the case of the Heisenberg\nferromagnet equation related to the same Lie algebra.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-27","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-2403.18165","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
We consider a matrix nonlinear partial differential equation that generalizes
Heisenberg ferromagnet equation. This generalized Heisenberg ferromagnet
equation is completely integrable with a linear bundle Lax pair related to the
pseudo-unitary algebra. This allows us to explicitly derive particular
solutions by using dressing technique. We shall discuss two classes of
solutions over constant background: soliton-like solutions and quasi-rational
solutions. Both classes have their analogues in the case of the Heisenberg
ferromagnet equation related to the same Lie algebra.
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