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

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.

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

“…Several approaches have been suggested, including the improved F-expansion method [7], the variational iteration method [8], the inverse scattering technique [9], the tanh-coth function technique [10], the Jacobi elliptic function expansion technique [11,12] and disciplines, and opened up new avenues. Many of the techniques created for the analysis of NLPDEs exhibit a level of sophistication that makes it challenging for many researchers to access them [14][15][16][17][18]. Today, in many different domains, including plasma physics, optics, biological systems, plasma physics, chemical systems, etc., NLPDEs are ubiquitous and have come to define them [19][20][21][22].…”

Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system

“…The objective of this research is to showcase results and recent developments in the theory of evolution equations, encompassing both theoretical and practical aspects. Many researchers and mathematicians have suggested a variety of efficient methods 1 – 6 for finding exact solutions of nonlinear (NPDEs), such as Hirota’s bilinear method 7 , tanh function method 8 , the inverse scattering technique 9 , the Bäcklund transformation method 10 , modified variational iteration method 11 , the multiple exp-function approaches 12 , the Darboux transformation approach 13 , the Lie symmetry analysis 14 – 16 , the -expansion approach 17 , the Kudryashov technique 18 and the Jacobi elliptic technique 19 – 21 .…”

Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons

“…Particularly interesting circumstances are modeled using nonlinear partial differential equations (NPDEs). Nonlinear wave phenomena are studied in a wide range of scientific and engineering fields, such as optical fibers, computational fluid dynamics, plasma physics, solid-state physics chemical dynamics, biological, and chemical-physical science, geochemistry, and shallow waves [4][5][6]. Nonlinear wave processes involving dissipation, dispersion, responses, convection, and propagation are crucial in understanding nonlinear wave equations [7][8][9].…”