Exploring Lie Point Symmetries and Exact Solutions for (1+1) Dimensional Modified Thomas and (1+2) Dimensional Chaffee-Infante Equations

Abstract

Lie symmetry analysis is a highly effective tool for finding exact solutions to differential equations, decreasing the number of independent variables, or at least reducing the equations order and nonlinearity. This article presents exact solutions for the (1+1)-dimensional modified Thomas and (1+2)-dimensional Chaffee-Infante equations through the application of the symmetry reduction method. These equations yield exact solutions under specific parametric conditions. Multiple exact solutions, such as periodic, soliton, and solitary wave solutions, along with newly found solitary wave solutions, are derived to validate their physical relevance. The findings are graphically illustrated with appropriate parametric settings, shown in both 2D and 3D. The outcomes of this study are expected to have applications across a wide range of scientific fields.