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 (17)

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• Exact Noncommutative Solitons
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Cited by in corpus (15)

• Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
• On integrable wave interactions and Lax pairs on symmetric spaces
• On nonlocal models of Kulish-Sklyanin type and generalized Fourier transforms
• Nonlocal reductions of the Ablowitz-Ladik equation
• On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
• Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces
• NLS-type equations from quadratic pencil of Lax operators: negative flows
• Linear hyperbolic PDEs with non-commutative time
• On soliton solutions and soliton interactions of Kulish-Sklyanin and Hirota-Ohta systems
• $G$-Strands on symmetric spaces
• Structure of Noncommutative Solitons: Existence and Spectral Theory
• Twisted hierarchies associated with the generalized sine-Gordon equation
• Dynamics of Noncommutative Solitons II: Spectral Theory, Dispersive Estimates and Stability
• Integrable systems on symmetric spaces from a quadratic pencil of Lax operators
• High energy bounds on wave operators