Potential Symmetries, One-Dimensional Optimal System and Invariant Solutions of the Coupled Burgers’ Equations

Abstract

In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers' equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers' equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers' equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers' equations.

Analysis of Dynamical Behavior of One-Dimensional Real Maps: An Executable Dynamical Programming Software Approach

“…Bai et al. [37] analyze the invariant solutions of Coupled Burgers' equations utilizing one-dimensional optimum systems. The ground-state energy and entropy for a one-dimensional Heisenberg chain with alternating D-terms are investigated by Xiang et al.…”

Conservation Laws and Travelling Wave Solutions for a Negative-Order KdV-CBS Equation in 3+1 Dimensions

“…These solutions explain a fundamental and significant physical phenomenon. The Chen-Lee-Liu equation, Sawada-Kotera equation, Boussinesq equation, and many more models have recently been studied using the Lie symmetry technique [29][30][31][32]. In 2017, Wazwaz investigated the (2+1)-dimensional modified KdV-Calogero-Bogoyavlenskii-Schiff equation to discover abundant solutions with various physical features [2].…”