Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+$$\end{document}1)-dimensional generalized Burgers system with the variable coefficients in a fluid

Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic flow, plasma astrophysics and ocean dynamics. In this paper, a (2+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+$$\end{document}1)-dimensional generalized Burgers system with the variable coefficients in a fluid is investigated. We obtain the Painlevé-integrable constraints of the system with respect to the variable coefficients. Based on the truncated Painlevé expansions, an auto-Bäcklund transformation is constructed, along with some soliton solutions. Via a truncated Painlevé expansions, certain multiple kink solutions are derived. Via a complex-conjugate transformation, some breather solutions, half-periodic kink solutions and hybrid solutions composed of the breathers and kink waves are seen.