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.