Phase plane analysis of the dust-acoustic waves for the Burgers equation in a strongly coupled dusty plasma

Phase plane analysis of dust-acoustic waves (DAWs) for the Burgers equation is investigated in a strongly coupled dusty plasma (SCDP) for the first time. The Burgers equation is obtained applying the reductive perturbation technique under the class of generalized hydrodynamic equations. The dynamical system of the Burgers equation is obtained using the traveling wave transfiguration. A phase plot containing a pair of heteroclinic orbits and a family of periodic orbits is presented for DAWs employing the concept of bifurcation theory through phase plane analysis. The analytical forms of kink and anti-kink wave solutions are derived by the tanh method. Analytical form of the periodic wave solution for the Burgers equation is derived for the first time in a SCDP. The parameters such as coupling parameter (Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma$$\end{document}), viscosity coefficient (η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$~\eta$$\end{document}), dust–neutral collisional frequency (νdn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _{dn}$$\end{document}), temperature of dusts (Td\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_d$$\end{document}) and speed of wave (v) have significant effects on the dust-acoustic kink, anti-kink and periodic wave solutions.