{"title":"磁性 II 型通用非线性演化方程。特定解","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":"{\"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}","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}
A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions
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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