Vector dark solitons with non-trivial periodic background

The article deals with the vector dark solitons for the defocusing N-component Manakov model. It is shown that the carrier wave of dark solitons is not only a monochromatic wave but also a composition of such waves. This is possible by the model having U(0,N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {U}}(0,N)$$\end{document}-symmetry. The corresponding n-soliton solutions with a non-trivial background as well as a simple method for getting them from formerly known ones are given.