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

NSF-CNPq关于孤子、可积理论和初始维度对称性的合作研究建议：这是一项在NSF-CNPq合作研究计划内提供旅行补助的建议。该项目将使国际和平协会、阿拉廷教授和教授之间的长期合作得以继续。L.A.Ferreira(圣保罗大学)和J.F.Gomes和A.H.Zimerman(圣保罗州立大学)就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进行了研究。合作者计划共同努力提高对二维和更高维度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。他们期望在以下问题上取得进展：理解从双哈密尔顿结构的变形中出现的新的可积模型(具有和不具有超对称性)；构造具有内部自由度的非阿贝尔Toda模型及其孤子解；Riemann-Hilbert分解问题适用于由Witten-Dijkgraff-Verlinde-Verlinde方程描述的拓扑场理论的齐次梯度和tau函数之外的梯度；以及高维可积模型的孤子解及其结构。所提议的活动所产生的更广泛的影响在教育部分。它的目标是培训年轻的研究人员学习可积系统理论及其应用的新方法和新技术。在费雷拉博士、戈姆斯博士和齐默曼博士所在的巴西机构中有大量的研究生。旅行补助金将包括所有资深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位，并继续为这一领域做出贡献。

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.