Lie symmetry analysis, numerical solutions by spectral method and travelling wave solutions of a (5+1)-dimensional partial differential equation

Abstract

ABSTRACT The purpose of this research is to investigate the Lie symmetries and the numerical solution of the (5 + 1)-dimensional evolutionary differential equation using the Chebyshev spectral method. Also, the exact solution of this equation is presented by the traveling wave method. These equations play a very important role in mathematical physics and engineering sciences. The implemented algorithm is quite efficient and practically suitable for these problems. The use of Maple and MATLAB software allows us to perform complex and boring calculations. The most distinctive aspect of this method is that no prescribed assumptions are required, and enormous computational effort is reduced and rounding errors are avoided. Our proposed methods for checking and solving the considered equation show that this method is very accurate and practical.