Multi-solitons of Thermophoretic Motion Equation Depicting the Wrinkle Propagation in Substrate-Supported Graphene Sheets

Abstract

The paper addresses the thermophoretic motion (TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries (KdV) equation. The generalized unified method is capitalized to construct wrinkle-like multiple soliton solutions. Graphical analysis of one, two, and three-soliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.

Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation

“…There is a family of periodic trajectories of the planar dynamical system (22) surrounding the equilibrium point E 1 (u 1 , 0). Thus, we have a collection of periodic wave solutions that correspond to the collection of periodic trajectories surrounding E 1 (0, 0) of the system (22). One of the periodic waves of the GKdVE (1) is shown numerically in Figure 2 for 0 = 0.4 and c = 1.…”

“…The solitary wave of the GKdVE (1) corresponding the homoclinic trajectory at the singular point E 0 (0, 0) of the dynamical system (22) is obtained from the Hamiltonian function (23) and the dynamical system (22) as:…”

“…Because FEM is most widely used numerical scheme for solving mathematical models where we can discretize the whole problem into smaller parts called as finite elements [10]. The discretization of a boundary value problem results in a system of algebraic equations which is further solved [11][12][13][14][15][16][17][18][19][20][21][22][23]. Organization of this paper will be as follows: after a detailed introduction about tsunamis in Section 1, Section 2 reports the mathematical model under deliberation.…”

Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

“…In doing so, various solitons and solutions of the equations will be realized and further depicted graphically to confirm their shapes. One can well see various analytical and numerical methods used in tackling different forms of the Korteweg-de Vries equations and evolution equations in the papers cited above and also in [57][58][59][60][61]. The current paper is organized as follows: Sect.…”

Optical solitons of space-time fractional Fokas–Lenells equation with two versatile integration architectures

“…The importance of solitons is due to their presence in a variety of nonlinear differential equations portraying many complex nonlinear phenomena, including acoustics, nonlinear optics, telecommunication industry, convictive fluids, plasma physics, condensed matter, and solid-state physics. Nonlinear Schrödinger's equation and its variant forms are used in dispersive mediums in different fields of mathematical physics and have been studied mathematically in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”