Some Soliton Hierarchies Associated with Lie Algebras $$\mathfrak {sp}(4)$$ and $$\mathfrak {so}(5)$$

IF 1.4 4区物理与天体物理 Q2 MATHEMATICS, APPLIED

Journal of Nonlinear Mathematical Physics Pub Date : 2023-09-26 DOI:10.1007/s44198-023-00140-6

Baiying He, Shiyuan Liu, Siyu Gao

{"title":"Some Soliton Hierarchies Associated with Lie Algebras $$\\mathfrak {sp}(4)$$ and $$\\mathfrak {so}(5)$$","authors":"Baiying He, Shiyuan Liu, Siyu Gao","doi":"10.1007/s44198-023-00140-6","DOIUrl":null,"url":null,"abstract":"Abstract Based on the symplectic Lie algebra $$\\mathfrak {sp}(4)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>sp</mml:mi> <mml:mo>(</mml:mo> <mml:mn>4</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , we obtain two integrable hierarchies of $$\\mathfrak {sp}(4)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>sp</mml:mi> <mml:mo>(</mml:mo> <mml:mn>4</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and by using the trace identity, we give their Hamiltonian structures. Then, we use $$2\\times 2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> Kronecker product, and construct integrable coupling systems of one soliton equation. Next, we consider two bases of Lie algebra $$\\mathfrak {so}(5)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>so</mml:mi> <mml:mo>(</mml:mo> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and we get the corresponding two integrable hierarchies. Finally, we discuss the relation between the integrable hierarchies of two different bases associated with Lie algebra $$\\mathfrak {so}(5)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>so</mml:mi> <mml:mo>(</mml:mo> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> .","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s44198-023-00140-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

Abstract Based on the symplectic Lie algebra $$\mathfrak {sp}(4)$$ sp ( 4 ) , we obtain two integrable hierarchies of $$\mathfrak {sp}(4)$$ sp ( 4 ) , and by using the trace identity, we give their Hamiltonian structures. Then, we use $$2\times 2$$ 2 × 2 Kronecker product, and construct integrable coupling systems of one soliton equation. Next, we consider two bases of Lie algebra $$\mathfrak {so}(5)$$ so ( 5 ) , and we get the corresponding two integrable hierarchies. Finally, we discuss the relation between the integrable hierarchies of two different bases associated with Lie algebra $$\mathfrak {so}(5)$$ so ( 5 ) .

查看原文本刊更多论文

与李代数相关的一些孤子层次$$\mathfrak {sp}(4)$$及 $$\mathfrak {so}(5)$$

摘要基于辛李代数$$\mathfrak {sp}(4)$$ sp(4)，得到了$$\mathfrak {sp}(4)$$ sp(4)的两个可积层次，并利用迹恒等式给出了它们的哈密顿结构。然后利用$$2\times 2$$ 2 × 2 Kronecker积，构造了单孤子方程的可积耦合系统。接下来，我们考虑了李代数$$\mathfrak {so}(5)$$ so(5)的两个基，得到了对应的两个可积层次。最后，我们讨论了与李代数相关的两种不同基的可积层次之间的关系$$\mathfrak {so}(5)$$ so(5)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics