Symmetries and Soliton Solutions of Integrable Models

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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.