Eur. Phys. J. Plus (2019) 134: 303
https://doi.org/10.1140/epjp/i2019-12679-9

Regular Article

Solitons and lump wave solutions to the graphene thermophoretic motion system with a variable heat transmission

¹ Department of Mathematics, NCBA&E, LBU DHA Campus, Lahore, Pakistan
² Department of Mathematics and Statistics, The University of Lahore, 54000, Lahore, Pakistan
³ Institute of Chemistry, University of the Punjab, 54790, Lahore, Pakistan
⁴ Department of Basic Science, Faculty of Engineering at October 6 University, 6th of October, Cairo, Egypt
⁵ Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Islamabad, Pakistan

^* e-mail: younis.pu@gmail.com

Received: 24 February 2019
Accepted: 7 April 2019
Published online: 27 June 2019

Abstract

Graphene is one of the thinnest and hardest elastic nanoscale materials and has opened new horizons in the field of material science for its versatile applications. The thermophoretic motion system is under investigation which describes the propagation of solitons in substrate-supported graphene sheets. A test function of the extended three-soliton method is used to construct the new soliton solutions. The one-order and mixed-order solutions involving solitons and lump waves are constructed. The dynamical behaviour of solitons under reflection, periodic distribution and interaction is depicted. Moreover, the bright and mixed type lump wave soliton propagation and interaction are discussed.