NSF-CNPq Collaborative Research Proposal on solitons, integrable theories and inifite-dimensional symmetries

NSF-CNPq 关于孤子、可积理论和无限维对称性的合作研究提案

• 批准号: 0651694
• 负责人: Henrik Aratyn
• 金额: --
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0651694&HistoricalAwards=false
• 关键词: NSF; CNPq; Collaborative; Research; Proposal

NSF-CNPq Collaborative Research Proposal on solitons, integrable theoriesand inifite-dimensional symmetries:This is a proposal for a travel grant within the NSF-CNPq Collaborative Researchprogram. The project will enable continuation of a long-term collaboration of the PI,Professor Aratyn, with Profs. L.A. Ferreira (University of Sao Paulo), and J.F. Gomesand A.H. Zimerman (State University of Sao Paulo) on fundamental features ofintegrability and further development of its applications in a variety of modern physicalcontexts.The collaborators plan to combine efforts to improve knowledge of various integrablemodels in two and higher dimensions, their algebraic and analytic aspects and tiesbetween them. They expect to make advances on the following topics: understandingof new integrable models (with and without supersymmetry) emerging fromdeformations of bihamiltonian structures; construction of non-abelian Toda models withinternal degrees of freedom and its soliton solutions; the Riemann-Hilbert factorizationproblem applied to gradations other than the homogeneous ones and the tau functionsof topological field theories described by the Witten-Dijkgraff-Verlinde-Verlinde equation;and soliton solutions of higher-dimensional integrable modelsand their structure.The broader impacts resulting from the proposed activity are in the educationalcomponent. Its objectives are to train young researchers in new methods andtechniques of the theory of integrable systems and their applications. There are a largenumber of graduate students in the Brazilian hosts institutions of Drs. Ferreira, Gomesand Zimerman The travel grant will involve all senior collaborators in training andmentoring arrangements. Several former Brazilian students and one US student nowhold academic positions and continue to contribute to the field.

关于孤子、可积理论和无限维对称性的 NSF-CNPq 合作研究提案：这是 NSF-CNPq 合作研究计划内的旅行补助金提案。该项目将使 PI Aratyn 教授与教授们继续长期合作。 L.A. Ferreira（圣保罗大学）和 J.F. Gomes 和 A.H. Zimerman（圣保罗州立大学）讨论可积性的基本特征及其在各种现代物理环境中的应用的进一步发展。合作者计划共同努力，提高对各种可积模型的了解在二维及更高维度中，它们的代数和分析方面以及它们之间的联系。他们期望在以下主题上取得进展：理解从双哈密尔顿结构的变形中出现的新的可积模型（具有或不具有超对称性）；内部自由度非阿贝尔 Toda 模型及其孤子解的构造； Riemann-Hilbert 分解问题应用于齐次级以外的等级以及由 Witten-Dijkgraff-Verlinde-Verlinde 方程描述的拓扑场论的 tau 函数；以及高维可积模型的孤子解及其结构。拟议的活动属于教育部分。其目标是培养年轻研究人员可积系统理论及其应用的新方法和技术。巴西博士所在院校有大量研究生。 Ferreira、Gomes 和 Zimerman 差旅补助金将让所有高级合作者参与培训和指导安排。几名前巴西学生和一名美国学生现在担任学术职务，并继续为该领域做出贡献。