Investigating the Lie symmetry method for generalized modified heat‎ ‎equation

Lie theory, was pioneered by mathematician Sophus Lie. Caprasse, and Élie Cartan, have evolved into a powerful mathematical framework for understanding the symmetries inherent in differential equations. Employing Lie group analysis, we aim to systematically explore the inherent symmetries of the nonlinear PDE. This analysis provides valuable insights into the invariance properties, unveiling hidden structures that can contribute to a deeper understanding of the equation. Through the scrutiny of Lie symmetries, our objective is to facilitate the identification of exact solutions for the nonlinear PDE. This contributes to the development of analytical methods and enhances our ability to comprehend the physical implications of the solutions.

Keywords:

Generalized modified heat equation‎ , ‎Lie symmetry method‎ , invariant‎ ‎solution‎ , Exact solution