# Algebraic and Analytic Aspects of Soliton Type Equations

@article{Gerdjikov2002AlgebraicAA,
title={Algebraic and Analytic Aspects of Soliton Type Equations},
journal={arXiv: Exactly Solvable and Integrable Systems},
year={2002}
}
• V. Gerdjikov
• Published 11 June 2002
• Mathematics
• arXiv: Exactly Solvable and Integrable Systems
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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