Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission

Abstract

Graphene has appeared as one of the most promising nanomaterials with unique thermal, electronic and mechanical properties which make it suitable for many applications in materials science, energy storage, electronics, water filtration and medicine. In this paper, we have studied the (2+1)-dimensional graphene sheets (GS) equation with variable heat transmission thermophoretic motion by using both Bäcklund transformation and similarity reduction techniques. As a result, from Bäcklund transformation one soliton solution was obtained and from similarity reduction technique the GS equation is reduced to a nonlinear ordinary differential equation which can be solved using the trial equation method; where many novel wave solutions were obtained. As an additional remark, the Bäcklund transformation obtained can be found by the traditional Painléve test. Finally, some graphs are given to illustrate the effect of the variable coefficients on the behavior of the thermal wave transmission.