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

Abstract

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 ${\mathbf{B}}_r\simeq so(2r+1,\mathbb{C})$ type.

References in corpus (4)

• Multicomponent Bright Solitons in F = 2 Spinor Bose-Einstein Condensates
• Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type
• Basic aspects of soliton theory
• New Integrable Multi-Component NLS Type Equations on Symmetric Spaces: Z_4 and Z_6 Reductions

Cited by in corpus (2)

• Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
• Twisted hierarchies associated with the generalized sine-Gordon equation