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：这是NSF-CNPq合作研究计划中旅行资助的提案。该项目将使PI， Aratyn教授与教授的长期合作得以延续。L.A. Ferreira（圣保罗大学）和J.F. Gomesand A.H. zimmerman（圣保罗州立大学）就不可整合性的基本特征及其在各种现代物理环境中应用的进一步发展进行了研究。合作者计划联合努力来提高二维和高维的各种可积模型的知识，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：理解由比哈密顿结构变形产生的新的可积模型（有或没有超对称）；非阿贝尔内自由度Toda模型的构造及其孤子解黎曼-希尔伯特分解问题适用于除齐次层次以外的层次，以及由witten - dijkgraffv - verlinde - verlinde方程描述的拓扑场论中的tau函数；高维可积模型的孤子解及其结构。拟议的活动所产生的更广泛的影响是在教育方面。其目标是在可积系统理论及其应用的新方法和新技术方面培养年轻的研究人员。在巴西的博士院校有大量的研究生。旅行补助将包括所有高级合作者的培训和指导安排。几名前巴西学生和一名美国学生现在拥有学术职位，并继续为该领域做出贡献。

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.