# Algebraic and Analytic Aspects of Soliton Type Equations

@article{Gerdjikov2002AlgebraicAA, title={Algebraic and Analytic Aspects of Soliton Type Equations}, author={Vladimir S Gerdjikov}, journal={arXiv: Exactly Solvable and Integrable Systems}, year={2002} }

This is a review of two of the fundamental tools for analysis of soliton equations: i) the algebraic ones based on Kac-Moody algebras, their central extensions and their dual algebras which underlie the Hamiltonian structures of the NLEE; ii) the construction of the fundamental analytic solutions of the Lax operator and the Riemann-Hilbert problem (RHP) which they satisfy. The fact that the inverse scattering problem for the Lax operator can be viewed as a RHP gave rise to the dressing Zakharov…

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