Abstract
In the current decade, nanomaterials have attracted great attention due to the wide range of applications in various disciplines and nanotechnology. Graphene is the best nanoscale material and one of the thinnest elastic films and has various applications. The thermophoretic motion system describes the diffusion of solitaries into substrate-supported graphene sheets. Lie group transformation of the motion equation is used to reduce the equation into solvable equation which is solved through the Bernoulli approximation method and some properties of the solutions are discussed.
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