No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Multiple-Lump Waves and Their Breaking Properties for a Thermophoretic Motion System in a Graphene Sheet
Abstract
A thermophoretic motion system with a variable heat transmission factor is investigated, which describes wrinkling soliton propagation in a substrate-supported graphene sheet. Analytic multiple-lump wave solutions are constructed via the Hirota bilinear method and symbolic computation. A numerical simulation shows that the system exhibits breaking lump waves. The system parameters control the open width and number of breaking gaps. These results should contribute to a better understanding of the propagation characteristics of wrinkling solitons in a complex graphene thermophoretic motion system.
... Several methods, such as inverse scattering, Hirota's bilinear approach, and its streamlined version, variational approach [17], and multiple-solitary wave solutions have been developed to examine the integrability of nonlinear partial differential equations. Equation (3) was used to understand the wave propagation of the N-soliton solutions in [18,19]. These results were obtained using symbolic computations and Hirota's bilinear technique. ...
This article discusses the thermophoretic motion (TM) equation that is used to describe soliton-like thermophoresis of wrinkles in Graphene sheets 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.
... General, rogue wave appears from nowhere and disappears with a trace [17]. Moreover, rogue wave have marvelous applications in various areas of science such as optical fiber, ocean engineering, graphene, ferrite, atmosphere, water tank, plasma [18][19][20][21][22][23][24][25]. ...
In this research, we study the dispersive phenomena for the (2+1)-dimensional generalized breaking soliton system (GBSS), which describe the interaction phenomena between Rieman wave and long wave via two space variable in nonlinear media. The constructed solitary wave results for the (2+1)-dimensional GBSS via extended modified rational expansion (EMRE) method in the form of rational, elliptic, and trigonometric functions including mixed solitons, single bright and dark solitions, combined bright and dark solitons, kink and anti-kink wave solitions, traveling waves, and periodic waves. The physical phenomena of demonstrated results represented by higher dimensional and contour plots graphically with the help of symbolic computation. The obtained results are very helpful in the study of interaction phenomena in fiber optics, mathematical physics, fluid dynamics, geophysics, engineering and many other various areas of scientific fields.
... Till now, the researchers, who study this subject, have great attention to soliton and lump waves, but most of them work experimentally [Guo and Guo, 2013;Panizona et al., 2017;Deng and Berry, 2016]. Ma and Li [2018] proposed N-solutions by using the bilinear method, Arif et al. [2019] proposed the new soliton solutions by the extended three-soliton method and Li et al. [2018] gave analytic multiple-lump wave solutions via the Hirota bilinear method and symbolic computation. ...
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.
... Many methods are used to obtain the soliton solutions for nonlinear evolution equations (NLEEs), such as G ′ ∕G-expansion method, 50-52 direct method, 53 Bäcklund transformation method, 54,55 auxiliary equation method, [56][57][58] Riccati mapping method, 59,60 and Hirota bilinear transformation method. [61][62][63][64][65][66][67][68][69][70] The Hirota bilinear transformation method is a classical symbolic scheme to seek for the soliton and multiple soliton solutions. Its critical idea is to transform the nonlinear problem to two or multiple linear ones. ...
A bilinear transformation method is proposed to find the rogue wave solutions for a generalized fourth‐order Boussinesq equation, which describes the wave motion in fluid mechanics. The one‐ and two‐order rogue wave solutions are explicitly constructed via choosing polynomial functions in the bilinear form of the equation. The existence conditions for these solutions are also derived. Furthermore, the system parameter controls on the rogue waves are discussed. The three parameters involved in the equation can strongly impact the wave shapes, amplitudes, and distances between the wave peaks. The results can be used to deeply understand the nonlinear dynamical behaviors of the rogue waves in fluid mechanics.
Graphene can be considered as the material used for many electronic devices. This is due to its excellent physical and chemical properties, which have been studied and implemented from a theoretical basis. The study of graphene-based devices for thermal energy conversion is of great interest. The investigation of the behavior of thermal wave transmission occupied a remarkable area of research in the literature. In these works attention was focused to (1 + 1) dimensional grahene sheet GS, where the governing equation is non autonomous. Here,we construct an extension to the (1 + 1) dimensional thermophoretic waves transmission model equation to (2 + 1) dimensional case. This problem is completely original. The coefficients of the constructed equation are time dependent, so an elaborated method is needed. To this issue, the extended unified method is used to find the exact solutions, in polynomial and rational forms. It is shown that the solutions obtained exhibit a transmission of multi -geometric thermophoretic waves structures, which are new when comparing with those existing in the literature which lumps or wrinkle solitons. Among them, wrinkle chirped, hybrid chirped, complex M-shaped, hybrid-M-shaped, wrinkle solitons, lattice waves, and sink-shape lump waves. Further chaotic termophoretic motion is shown to occur. Also, the effects of thermal conductive coefficients are investigated. Further the stability analysis shows that the TW motion is asymptotically stable.
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.
A (2+1)-dimensional generalized breaking soliton system is under investigation, which can be used to describe the interaction between Riemann wave and long wave along with two space directions in nonlinear media. Rogue wave solutions, two types of mixed soliton and rogue wave solutions are constructed through appropriately choosing the functions in the bilinear forms. The rogue wave structures and the interaction characteristics between the soliton and rogue wave are studied in details. Novel hidden rogue wave and hidden soliton, which are invisible but work, are observed during the interactions.
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 uni ed 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
A generalized Schrödinger equation in an inhomogeneous optical fiber system is investigated, which is with variable gain coefficient, variable dispersion coefficient and variable nonlinearity coefficient. Analytical soliton solution and its compatible condition are derived by using the auxiliary equation method. Through setting the dispersion function and gain function, the periodic, doubly periodic, and N-kink-like solitons are excited and observed.
ResearchGate has not been able to resolve any references for this publication.