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Zbl 1101.35069
Gerdjikov, Vladimir S.; Kaup, David J.
How many types of soliton solutions do we know? (English)
[A] Mladenov, Iva\"ilo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2--10, 2005. Sofia: Bulgarian Academy of Sciences. 11-34 (2006). ISBN 954-8495-30-9/pbk

Summary: We discuss several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations 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 ${\germ {sl}}(p)$, $2\le p\le n$ of ${\germ{sl}}(n)$, a type of one-soliton solutions which have $p-1$ internal degrees of freedom.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
37K30 Relations with algebraic structures
37K15 Integration by inverse spectral and scattering methods
35Q51 Solitons

Keywords: multicomponent nonlinear Schrödinger equation; Lax representation; Zakharov-Shabat system; inverse scattering method

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