Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets

Abstract

Abstract This article discusses the thermophoretic motion (TM) equation that is used to describe soliton-like thermophoresis of wrinkles in Graphene sheet based on the Korteweg–de Vries (KdV) equation. Wrinkle-like exact solutions are constructed using the Lie group method and modified auxiliary equation (MAE) approach. A graphic analysis of the solutions is done to show how various parameters may change the attributes of the solutions, such as breadth, amplitude, shape, and open direction.