Mathematical Sciences: Algebraic Methods in Nonlinear Problems

本研究的主题是可积系统的代数和几何结构以及李代数的作用。对双线性恒等式进行了解析解释，该恒等式在可积系统中的tau函数理论、顶点算符和场论方法中起着重要的作用。研究人员将研究陶氏法与扎哈罗夫和沙巴特的敷料法之间的关系。可能的应用是tau函数理论到其他可积系统的推广，包括多维问题。对可积系统的研究旨在提高我们对某些具有能量守恒性质的物理现象，如孤子的本质的理解。

The topic of this research is the algebraic and geometric structure of integrable systems and the role of Lie algebras. An analytical interpretation of the bilinear identity, which plays a fundamental role in the theory of tau function, vertex operators, and field theoretic methods of the Kyoto school in integrable systems is sought. The investigator will study the relationship between the tau method and the dressing method of Zakharov and Shabat. Possible applications are an extensions of the theory of tau function to other integrable systems, including multidimensional problems. The study of integrable systems is aimed at improving our understanding the nature of certain physical phenomena that have the properties of energy preservation, such as solitons.