Lie Symmetries and Exact Solutions of KdV–Burgers Equation with Dissipation in Dusty Plasma

This article investigates nonlinear behavior of ion acoustic waves in a plasma with superthermal electrons and isothermal positrons. We consider the KdV–Burgers equation with dissipation in dusty plasmas and construct Lie symmetries, infinitesimal generators and commutative relations under invariance property of Lie groups of transformations. The adjoint relations and invariant functions lead to one dimensional optimal system. We derive similarity variables by using Lie group analysis, where the KdV–Burgers equation reduces in over determined equations, which provide exact solutions. The solutions are absolutely new and more general than previous results (Fan et al. in Phys Lett A 17:376–380, 2001; Feng and Wang in Phys Lett A 308:173–178, 2003; Cimpoiasu in Roam J Phys 59:617–624, 2014; Arora and Chauhan in Int J Appl Comput Math 5:1–13, 2019) as that contain both the arbitrary functions f1(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_1(t)$$\end{document} and f2(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_2(t)$$\end{document} as well as arbitrary constants. Due to existence of arbitrary constants and functions that may describe rich physical behavior. We discuss these solutions corporeally with their numerical simulation. Consequently, parabolic, elastic multi-soliton, compacton and their annihilation profiles are discussed systematically to make these findings more worthy.