Exact Solutions of the Two-Dimensional Cattaneo Model Using Lie Symmetry Transformations

Abstract

In this article, symmetry technique is utilized to obtain new exact solutions of the Cattaneo equation. The infinitesimal symmetries, linear combinations of these symmetries, and corresponding similarity variables are determined, which lead to many exact solutions of the considered equation. By applying similarity transformations, the mentioned partial differential equation is reduced to some ordinary differential equations of second order. Solutions of these ordinary differential equations have yielded many exact solutions of the Cattaneo equation.

New Explicit Solutions of Zoomeron Equation Using Optimal Indexing Approach

“…In [9] and [10] Khalil and Khadija used the power index method to find new exact solutions of the Ablowitz-Kaup-Newell-Segur water wave equation and Burger's equation. Transformations of variables can sometimes be found that transform a nonlinear PDE into a nonlinear ODE such as Lie Symmetry Transformations [11], [12]. The phenomenon of a soliton with constant shape and speed was proposed by Russell in 1834, which he called a translational wave [8].…”