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

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

2010-06-02

arxiv.org/abs/1006.0301v1

SIGMA 6 (2010), 044, 29 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.3842/SIGMA.2010.044

The algebraic structure and the spectral properties of a special class of multi-component NLS equations, related to the symmetric spaces of {\bf 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 $\mathfrak{g}$. Special attention is paid to the structure of the dressing factors in spinor representation of the orthogonal simple Lie algebras of ${\bf B}_r\simeq so(2r+1,{\mathbb C})$ type.

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