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The algebraic structure and the spectral properties of a special class of multicomponent 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 associated Lax operator to these nonlinear evolutionary equations for different fundamental representations of the underlying simple Lie algebra g. Special attention is paid to the spinor representation of the orthogonal Lie algebras of B type.
Gerdjikov, V.S. & Grahovski, G.G. (2010). Multi-component NLS Models on Symmetric Spaces:Spectral Properties versus Representations Theory. SIGMA, vol. 6, article 044. doi:10.21427/hke1-rm28