Abstract
Lie symmetry analysis of differential equations proves to be a powerful tool to solve or at least reduce the order and nonlinearity of the equation. Symmetries of differential equations is the most significant concept in the study of DE’s and other branches of science like physics and chemistry. In this present work, we focus on Lie symmetry analysis to find symmetries of some general classes of KS-type equation. We also compute transformed equivalent equations and some invariant solutions of this equation.
Highlights
Symmetry has been a source of inspiration as a powerful tool in the formulation of the laws of the universe
A great number of physical phenomena is transformed into differential equations
The symmetry group approach is well-known for its importance in the field of differential equations analysis
Summary
Symmetry has been a source of inspiration as a powerful tool in the formulation of the laws of the universe. The principal paper on Lie symmetry is [1], in which Lie demonstrated that a linear 2D, 2nd-order PDE admits at most three boundary invariance group He processed the maximal invariance group of the onedimensional heat conductivity and used this analysis to compute its explicit solutions. We deal with the generalized modified one-dimensional Kuramoto-Sivashinsky (GMKS) type equation and determine the symmetry algebra by using Lie symmetry analysis. The Kuramoto-Sivashinsky equation gives the change of the position of a flame front (Figure 1) It shows the flame front position against time for horizontally propagating methane flame, the movement of a fluid going down a vertical wall, or a spatially uniform oscillating chemical reaction in a homogeneous medium [16].
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