## Proceedings of the International Conference on Geometry, Integrability and Quantization

### On the Multi-Component NLS Type Equations on Symmetric Spaces: Reductions and Soliton Solutions

#### Abstract

The fundamental properties of the multi-component nonlinear Schrödinger (MNLS) type models related to symmetric spaces are analyzed. New types of reductions of these systems are constructed. The Lax operators $L$ and the corresponding recursion operators $\Lambda$ are used to formulate some of the fundamental properties of the MNLS-type equations. The results are illustrated by specific examples of MNLS-type systems related to the D.III symmetric space for the $\mathfrak{so}(8)$-algebra. The effect of the reductions on their soliton solutions is outlined.

#### Article information

Dates
First available in Project Euclid: 12 June 2015

https://projecteuclid.org/ euclid.pgiq/1434148350

Digital Object Identifier
doi:10.7546/giq-6-2005-203-217

Mathematical Reviews number (MathSciNet)
MR2161767

Zentralblatt MATH identifier
1079.53075

#### Citation

Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A. On the Multi-Component NLS Type Equations on Symmetric Spaces: Reductions and Soliton Solutions. Proceedings of the Sixth International Conference on Geometry, Integrability and Quantization, 203--217, Softex, Sofia, Bulgaria, 2005. doi:10.7546/giq-6-2005-203-217. https://projecteuclid.org/euclid.pgiq/1434148350