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VOL. 7 | 2006 How Many Types of Soliton Solutions do We Know?
Vladimir S. Gerdjikov, David J. Kaup

Editor(s) Ivaïlo M. Mladenov, Manuel de León


We discuss several ways of how one could classify the various types of soliton solutions related to NLEE that are solvable with the generalized $n \times n$ Zakharov–Shabat system. In doing so we make use of the fundamental analytic solutions, the dressing procedure and other tools characteristic for the inverse scattering method. We propose to relate to each subalgebra $\mathfrak{sl}(p), 2 \leq p \leq n$ of $\mathfrak{sl}(n)$, a type of one-soliton solutions which have $p − 1$ internal degrees of freedom.


Published: 1 January 2006
First available in Project Euclid: 13 July 2015

zbMATH: 1101.35069
MathSciNet: MR2228361

Digital Object Identifier: 10.7546/giq-7-2006-11-34

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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