Symmetries and Soliton Solutions of Integrable Models

该项目的技术基础上的领域的代数方法，以获得实际的结果感兴趣的理论物理和基于孤子的光通信。该提案的主题之一涉及的建设的多分量KP族从单分量KP族和利用一个特殊的无限集的阿贝尔附加对称。 从应用的角度看，这导致了获得描述（2+1）维孤子的新的朗斯基解的前景。代数方法的tau函数和孤子解决方案的背景下表示的非常规分级的卡茨-穆迪李代数也将进行调查。 第三个主题是在可积模型的框架下建立超对称性并寻找相应的超对称孤波。最近，在将可积性概念扩展到高维模型方面取得了一些进展。 我们计划研究这种形式的可积性和高维孤子解之间的联系。 在高维模型中出现的类弦孤子结构是非常有意义的，并且可以在凝聚态物理和规范场理论的各种物理模型中找到应用。

This project bases its techniques on the field of algebraic methods to obtain practical results of interest for theoretical physics and soliton based optical communication.One of the topics of this proposal deals with construction of the multi-component KP hierarchies starting from one-component KP hierarchy and utilizing a special infinite set of abelian additional symmetries. From an application point of view, this leads to the prospect of obtaining new Wronskian solutions describing (2+1)-dimensional solitons. The algebraic approach to the tau-function and soliton solutions in the context of representations of Kac-Moody Lie algebras with unconventional grading will also be investigated. The third topic of this proposal involves the formulation of supersymmetry in the framework of integrable models and finding the corresponding supersymmetric solitary waves.Recently, some advances have been made with extending the notion of integrability to higher dimensional models. We plan to study connections between this form of integrability and higher dimensional soliton solutions. The emerging string-like soliton structures of higher dimensional models are quite intriquing and may find applications in various physical models of condensed matter physics and gauge field theory.