Proceedings of the International Conference on Geometry, Integrability and Quantization

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

Georgi G. Grahovski, Vladimir S. Gerdjikov, and Nikolay A. Kostov

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

Source
Proceedings of the Sixth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Allen C. Hirshfeld, eds. (Sofia: Softex, 2005), 203-217

Dates
First available in Project Euclid: 12 June 2015

Permanent link to this document
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


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