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

Abstract

The single-layer graphene flakes is the amazing thing in recent industry, it has many uses in biosensors, photonics and water filtration because of it is outstanding electronic, thermal, and mechanical properties. In this letter, we have studied the graphene variable heat transmission thermophoretic motion (vcGT) equation using 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 literature 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.