Symmetry transformations and novel solutions for the graphene thermophoretic motion equation with variable heat transmission using Lie group analysis

¹ Department of Physics, College of Science at Al-Zulfi, Majmaah University Majmaah 11952, Kingdom of Saudi Arabia
² Geomagnetic and Geoelectric Department, National Research Institute of Astronomy and Geophysics (NRIAG) 11421 Helwan, Cairo, Egypt
³ College of Business Administration in Majmaah, Majmaah University Majmaah 11952, Kingdom of Saudi Arabia
⁴ Department of Mathematics, Faculty of Education, Ain Shams University - Cairo, Egypt

Received: 4 November 2023
Accepted: 2 January 2024

Abstract

The single-layer graphene flake is an amazing tool in recent industry, it has many uses in biosensors, photonics and water filtration because of its outstanding electronic, thermal, and mechanical properties. In this letter, we have studied the graphene variable heat transmission thermophoretic motion (vcGT) equation using the symmetry group method. As a result, a Lie group of four vector fields is yielded. By using a linear combination of those vector fields the vcGT equation becomes a nonlinear ordinary differential equation, and by using the F-expansion technique then different types of solitary waves like periodic Jacobi elliptic waves, soliton, kink soliton and trigonometric waves were found which cover other solutions in the literature such as solitons and have additional new solutions like the periodic Jaocbi waves. Finally, we have discussed the effect of the variable heat transmission on the wave propagation for three different wave structures: Jacobi periodic wave, bright soliton and the trigonometric sec wave. It was found that in the real physical situation corresponding to the variable heat transmission the waves take a parabolic shape.