Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 044, 29 pages      arXiv:1006.0301      https://doi.org/10.3842/SIGMA.2010.044
Contribution to the Proceedings of the Eighth International Conference Symmetry in Nonlinear Mathematical Physics

Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory

Vladimir S. Gerdjikov a and Georgi G. Grahovski a, b
a) Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, Bulgaria
b) School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland

Received January 20, 2010, in final form May 24, 2010; Published online June 02, 2010

Abstract
The algebraic structure and the spectral properties of a special class of multi-component NLS equations, related to the symmetric spaces of BD.I-type are analyzed. The focus of the study is on the spectral theory of the relevant Lax operators for different fundamental representations of the underlying simple Lie algebra g. Special attention is paid to the structure of the dressing factors in spinor representation of the orthogonal simple Lie algebras of Br ≅ so(2r+1,C) type.

Key words: multi-component MNLS equations; reduction group; Riemann-Hilbert problem; spectral decompositions; representation theory.

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