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 meth...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 threesoliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.展开更多
The analytical solution of the multi-dimensional,time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transformdecompositionmethod is presented in this article.The aforesaidmodel is an...The analytical solution of the multi-dimensional,time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transformdecompositionmethod is presented in this article.The aforesaidmodel is analyzed by employing Caputo fractional derivative.We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods,respectively.The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems.The exact and estimated solutions are delineated via numerical simulation.The proposed analysis indicates that the projected configuration is extremely meticulous,highly efficient,and precise in understanding the behavior of complex evolutionary problems of both fractional and integer order that classify affiliated scientific fields and technology.展开更多
The generalized Riccati equation mapping method(GREMM)is used in this paper to obtain different types of soliton solutions for nonlinear Schrödinger equation with higher dimension that existed in the regimes of a...The generalized Riccati equation mapping method(GREMM)is used in this paper to obtain different types of soliton solutions for nonlinear Schrödinger equation with higher dimension that existed in the regimes of anomalous dispersion.Later,we use the q-homotopy analysis method combined with the Laplace transform(q-HATM)to obtain approximate solutions of the bright and dark optical solitons.The q-HATM illustrates the solutions as a rapid convergent series.In addition,to show the physical behavior of the solutions obtained by the proposed techniques,the graphical representation has been provided with some parameter values.The findings demonstrate that the proposed techniques are useful,efficient and reliable mathematical method for the extraction of soliton solutions.展开更多
The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958.This model(or system of equations)has intrinsic participation energy and materials sciences and depicts significant characteristics ...The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958.This model(or system of equations)has intrinsic participation energy and materials sciences and depicts significant characteristics of two phase systems relating to the procedures of phase separation when the temperature is constant.For instance,it can be noticed when a binary alloy(“Aluminum+Zinc”or“Iron+Chromium”)is cooled down adequately.In this case,partially or totally nucleation(nucleation means the appearance of nuclides in the material)is observed:the homogeneous material in the initial state gradually turns into inhomogeneous,giving rise to a very accurate dispersive microstructure.Next,when the time scale is slower the microstructure becomes coarse.In this work,to the first time,the unified method is presented to investigate some physical interpretations for the solutions of the Cahn-Hilliard system when its coefficients varying with time,and to show how phase separation of one or two components and their concentrations occurs dynamically in the system.Finally,2D and 3D plots are introduced to add more comprehensive study which help to understand the physical phenomena of this model.The technique applied in this analysis is powerful and efficient,as evidenced by the computational work and results.This technique can also solve a large number of higher-order evolution equations.展开更多
In this research article,the perturbed nonlinear Schrödinger equation(P-NLSE)is examined by utilizing two analytical methods,namely the extended modified auxiliary equation mapping and the generalized Riccati equ...In this research article,the perturbed nonlinear Schrödinger equation(P-NLSE)is examined by utilizing two analytical methods,namely the extended modified auxiliary equation mapping and the generalized Riccati equation mapping methods.Consequently,we establish several sorts of new families of complex soliton wave solutions such as hyperbolic functions,trigonometric functions,dark and bright solitons,periodic solitons,singular solitons,and kink-type solitons wave solutions of the P-NLSE.Using the mentioned methods,the results are displayed in 3D and 2D contours for specific values of the open parameters.The obtained findings demonstrate that the implemented techniques are capable of identifying the exact solutions of the other complex nonlinear evolution equations(C-NLEEs)that arise in a range of applied disciplines.展开更多
The(3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation,dynami...The(3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation,dynamics of shallow water wave,plasma fluid model,chemical kinematics,chemical engineering,geochemistry,and many other topics.In this article,we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in it.As a result,wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations,containing kink,breather soliton,bell-shaped soliton,and periodic waves.To extract the soliton solutions of the high-dimensional nonlinear evolution equations,a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions directly.The sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear equations.This study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension(HNEEs).Closed-form solutions are carefully illustrated and discussed through diagrams.展开更多
In this work,we use the(m+1/G')-expansion method and the Adomian decomposition method to study the 3D potential Yu-Toda-Sasa-Fukuyama(3D-pYTSF)equation which has a good application in the twolayer liquid medium.Fo...In this work,we use the(m+1/G')-expansion method and the Adomian decomposition method to study the 3D potential Yu-Toda-Sasa-Fukuyama(3D-pYTSF)equation which has a good application in the twolayer liquid medium.For the first time,the(m+1/G')-expansion and the Adomian decomposition methods are used to establish novel exact wave solutions and to study some numerical solutions for the 3D-pYTSF equation,respectively.Through using the analytical method,kink-type wave,singular solution and some complex solutions to the suggested equation are successfully revealed.The obtained wave solutions are represented with some figures in 3D and contour plots.展开更多
文摘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 threesoliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.
基金supported by the Natural Science Foundation of China(GrantNos.61673169,11301127,11701176,11626101,11601485).
文摘The analytical solution of the multi-dimensional,time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transformdecompositionmethod is presented in this article.The aforesaidmodel is analyzed by employing Caputo fractional derivative.We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods,respectively.The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems.The exact and estimated solutions are delineated via numerical simulation.The proposed analysis indicates that the projected configuration is extremely meticulous,highly efficient,and precise in understanding the behavior of complex evolutionary problems of both fractional and integer order that classify affiliated scientific fields and technology.
文摘The generalized Riccati equation mapping method(GREMM)is used in this paper to obtain different types of soliton solutions for nonlinear Schrödinger equation with higher dimension that existed in the regimes of anomalous dispersion.Later,we use the q-homotopy analysis method combined with the Laplace transform(q-HATM)to obtain approximate solutions of the bright and dark optical solitons.The q-HATM illustrates the solutions as a rapid convergent series.In addition,to show the physical behavior of the solutions obtained by the proposed techniques,the graphical representation has been provided with some parameter values.The findings demonstrate that the proposed techniques are useful,efficient and reliable mathematical method for the extraction of soliton solutions.
基金supported by Deanship of Scientific Re-search,Islamic University of Madinah(project Number:442/2020).
文摘The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958.This model(or system of equations)has intrinsic participation energy and materials sciences and depicts significant characteristics of two phase systems relating to the procedures of phase separation when the temperature is constant.For instance,it can be noticed when a binary alloy(“Aluminum+Zinc”or“Iron+Chromium”)is cooled down adequately.In this case,partially or totally nucleation(nucleation means the appearance of nuclides in the material)is observed:the homogeneous material in the initial state gradually turns into inhomogeneous,giving rise to a very accurate dispersive microstructure.Next,when the time scale is slower the microstructure becomes coarse.In this work,to the first time,the unified method is presented to investigate some physical interpretations for the solutions of the Cahn-Hilliard system when its coefficients varying with time,and to show how phase separation of one or two components and their concentrations occurs dynamically in the system.Finally,2D and 3D plots are introduced to add more comprehensive study which help to understand the physical phenomena of this model.The technique applied in this analysis is powerful and efficient,as evidenced by the computational work and results.This technique can also solve a large number of higher-order evolution equations.
文摘In this research article,the perturbed nonlinear Schrödinger equation(P-NLSE)is examined by utilizing two analytical methods,namely the extended modified auxiliary equation mapping and the generalized Riccati equation mapping methods.Consequently,we establish several sorts of new families of complex soliton wave solutions such as hyperbolic functions,trigonometric functions,dark and bright solitons,periodic solitons,singular solitons,and kink-type solitons wave solutions of the P-NLSE.Using the mentioned methods,the results are displayed in 3D and 2D contours for specific values of the open parameters.The obtained findings demonstrate that the implemented techniques are capable of identifying the exact solutions of the other complex nonlinear evolution equations(C-NLEEs)that arise in a range of applied disciplines.
基金The authors thank to Faculty of Science,University of Rajshahi,Bangladesh for supporting project number(TURSP-2019/16).
文摘The(3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation,dynamics of shallow water wave,plasma fluid model,chemical kinematics,chemical engineering,geochemistry,and many other topics.In this article,we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in it.As a result,wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations,containing kink,breather soliton,bell-shaped soliton,and periodic waves.To extract the soliton solutions of the high-dimensional nonlinear evolution equations,a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions directly.The sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear equations.This study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension(HNEEs).Closed-form solutions are carefully illustrated and discussed through diagrams.
基金Deanship of Scientific Re-search at Umm Al-Qura University for supporting this work by Grant Code:(22UQU4410172DSR06).
文摘In this work,we use the(m+1/G')-expansion method and the Adomian decomposition method to study the 3D potential Yu-Toda-Sasa-Fukuyama(3D-pYTSF)equation which has a good application in the twolayer liquid medium.For the first time,the(m+1/G')-expansion and the Adomian decomposition methods are used to establish novel exact wave solutions and to study some numerical solutions for the 3D-pYTSF equation,respectively.Through using the analytical method,kink-type wave,singular solution and some complex solutions to the suggested equation are successfully revealed.The obtained wave solutions are represented with some figures in 3D and contour plots.
