Mixed interactions of localized waves in the three-component coupled derivative nonlinear Schrödinger equations

The Darboux transformation of the three-component coupled derivative nonlinear Schrödinger equations is constructed. Based on the special vector solution generated from the corresponding Lax pair, various interactions of localized waves are derived. Here, we focus on the higher-order interactional solutions among higher-order rogue waves, multi-solitons, and multi-breathers. It is defined as the identical type of interactional solution that the same combination appears among these three components q1,q2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_1, q_2$$\end{document}, and q3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_3$$\end{document}, without considering different arrangements among them. According to our method and definition, these interactional solutions are completely classified as six types, among which there are four mixed interactions of localized waves in these three different components. In particular, the free parameters μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} and ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document} play the important roles in dynamics structures of the interactional solutions. For example, different nonlinear localized waves merge with each other by increasing the absolute values of these two parameters. Additionally, these results demonstrate that more abundant and novel localized waves may exist in the multi-component coupled systems than in the uncoupled ones.