In this paper, we prove the existence of the pullback attractor for the nonautonomous Benjamin-Bona-Mahony equations in H2 by establishing the pullback uniformly asymptotical compactness.
In this article, the application of variational homotopy perturbation method is applied to solve Benjamin-Bona-Mahony equation. Then, we obtain the numerical solution of BBM equation using the initial condition. Compa...In this article, the application of variational homotopy perturbation method is applied to solve Benjamin-Bona-Mahony equation. Then, we obtain the numerical solution of BBM equation using the initial condition. Comparison with Adomian’s decomposition method, homotopy perturbation method, and with the exact solution shows that VHPM is more effective and accurate than ADM and HPM, and is reliable and manageable for this type of equation.展开更多
New two-component vector breather solution of the modified Benjamin-Bona-Mahony(MBBM)equation is considered.Using the generalized perturbation reduction method,the MBBM equation is reduced to the coupled nonlinear Sch...New two-component vector breather solution of the modified Benjamin-Bona-Mahony(MBBM)equation is considered.Using the generalized perturbation reduction method,the MBBM equation is reduced to the coupled nonlinear Schr¨odinger equations for auxiliary functions.Explicit analytical expressions for the profile and parameters of the vector breather oscillating with the sum and difference of the frequencies and wavenumbers are presented.The two-component vector breather and single-component scalar breather of the MBBM equation is compared.展开更多
In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimati...In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.展开更多
In this paper, the ansatze method is implemented to study the exact solutions for the modified Benjamin-Bona-Mahony equation (mBBM). The singular-shaped traveling wave solution, the Bell-shape is traveling wave soluti...In this paper, the ansatze method is implemented to study the exact solutions for the modified Benjamin-Bona-Mahony equation (mBBM). The singular-shaped traveling wave solution, the Bell-shape is traveling wave solution, the kink-shaped traveling wave solution and the periodic traveling wave solution is obtained. With the assist of computational software MATLAB, the graphical exemplifications of solutions are illustrated of the two-dimension (2D) and three-dimension (3D) plots.展开更多
This paper is a discussion of global solutions to the initial value problems for general- ized Banjamin-Bona-Mahony equations.Some long time behaviors of the solutions are presented with the initial data in some certa...This paper is a discussion of global solutions to the initial value problems for general- ized Banjamin-Bona-Mahony equations.Some long time behaviors of the solutions are presented with the initial data in some certain Sobolev spaces.We employ the method of integral estimate, Fourier transform and Gronwall’s inequality.展开更多
We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations an...We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony equation.After substituting particular values of the parameters,different solitary wave solutions are derived from the exact traveling wave solutions.It is shown that these employed methods are more powerful tools for nonlinear wave equations.展开更多
In this article,semi-analytical and numerical simulations of the well-known modified Benjamin-Bona-Mahony(mBBM)equation are processed.This study targets to check the accuracy of the obtained analytical solutions of th...In this article,semi-analytical and numerical simulations of the well-known modified Benjamin-Bona-Mahony(mBBM)equation are processed.This study targets to check the accuracy of the obtained analytical solutions of the mBBM model that have been obtained in[1]through three recent analytical schemes(extended simplest equation(ESE)method,modified kudryashov(mKud)method,and SechTanh(ST)expansion method).The considered model describes the propagation of long waves in the nonlinear dispersive media in a visual illusion.The Homotopy iteration(HI)method,exponential cubic-B-spline(ECBS)method,and trigonometric-quantic-B-spline(TQBS)method are employed to construct novel semi-analytical and accurate numerical solutions.The obtained solutions’accuracy has been checked through some different types of two-dimensional graphs.展开更多
In this article,we suggest the two variable(G/G,1/G)-expansion method for extracting further general closed form wave solutions of two important nonlinear evolution equations(NLEEs)that model one-dimensional internal...In this article,we suggest the two variable(G/G,1/G)-expansion method for extracting further general closed form wave solutions of two important nonlinear evolution equations(NLEEs)that model one-dimensional internal waves in deep water and the long surface gravity waves of small amplitude propagating uni-directionally.The method can be regarded as an extension of the(G/G)-expansion method.The ansatz of this extension method to obtain the solution is based on homogeneous balance between the highest order dispersion terms and nonlinearity which is similar to the(G/G)method whereas the auxiliary linear ordinary differential equation(LODE)and polynomial solution differs.We applied this method to find explicit form solutions to the Burger’s and Benjamin-Bona-Mahony(BBM)equations to examine the effectiveness of the method and tested through mathematical computational software Maple.Some new exact travelling wave solutions in more general form of these two nonlinear equations are derived by this extended method.The method introduced here appears to be easier and faster comparatively by means of symbolic computation system.展开更多
基金supported by the NSF of China(11031003, 10871040)
文摘In this paper, we prove the existence of the pullback attractor for the nonautonomous Benjamin-Bona-Mahony equations in H2 by establishing the pullback uniformly asymptotical compactness.
文摘In this article, the application of variational homotopy perturbation method is applied to solve Benjamin-Bona-Mahony equation. Then, we obtain the numerical solution of BBM equation using the initial condition. Comparison with Adomian’s decomposition method, homotopy perturbation method, and with the exact solution shows that VHPM is more effective and accurate than ADM and HPM, and is reliable and manageable for this type of equation.
文摘New two-component vector breather solution of the modified Benjamin-Bona-Mahony(MBBM)equation is considered.Using the generalized perturbation reduction method,the MBBM equation is reduced to the coupled nonlinear Schr¨odinger equations for auxiliary functions.Explicit analytical expressions for the profile and parameters of the vector breather oscillating with the sum and difference of the frequencies and wavenumbers are presented.The two-component vector breather and single-component scalar breather of the MBBM equation is compared.
文摘In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.
文摘In this paper, the ansatze method is implemented to study the exact solutions for the modified Benjamin-Bona-Mahony equation (mBBM). The singular-shaped traveling wave solution, the Bell-shape is traveling wave solution, the kink-shaped traveling wave solution and the periodic traveling wave solution is obtained. With the assist of computational software MATLAB, the graphical exemplifications of solutions are illustrated of the two-dimension (2D) and three-dimension (3D) plots.
文摘This paper is a discussion of global solutions to the initial value problems for general- ized Banjamin-Bona-Mahony equations.Some long time behaviors of the solutions are presented with the initial data in some certain Sobolev spaces.We employ the method of integral estimate, Fourier transform and Gronwall’s inequality.
文摘We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony equation.After substituting particular values of the parameters,different solitary wave solutions are derived from the exact traveling wave solutions.It is shown that these employed methods are more powerful tools for nonlinear wave equations.
基金We greatly thank Taif University for providing fund for this work through Taif University Researchers Supporting Project num-ber(TURSP-2020/52)Taif University,Taif,Saudi Arabia.
文摘In this article,semi-analytical and numerical simulations of the well-known modified Benjamin-Bona-Mahony(mBBM)equation are processed.This study targets to check the accuracy of the obtained analytical solutions of the mBBM model that have been obtained in[1]through three recent analytical schemes(extended simplest equation(ESE)method,modified kudryashov(mKud)method,and SechTanh(ST)expansion method).The considered model describes the propagation of long waves in the nonlinear dispersive media in a visual illusion.The Homotopy iteration(HI)method,exponential cubic-B-spline(ECBS)method,and trigonometric-quantic-B-spline(TQBS)method are employed to construct novel semi-analytical and accurate numerical solutions.The obtained solutions’accuracy has been checked through some different types of two-dimensional graphs.
文摘In this article,we suggest the two variable(G/G,1/G)-expansion method for extracting further general closed form wave solutions of two important nonlinear evolution equations(NLEEs)that model one-dimensional internal waves in deep water and the long surface gravity waves of small amplitude propagating uni-directionally.The method can be regarded as an extension of the(G/G)-expansion method.The ansatz of this extension method to obtain the solution is based on homogeneous balance between the highest order dispersion terms and nonlinearity which is similar to the(G/G)method whereas the auxiliary linear ordinary differential equation(LODE)and polynomial solution differs.We applied this method to find explicit form solutions to the Burger’s and Benjamin-Bona-Mahony(BBM)equations to examine the effectiveness of the method and tested through mathematical computational software Maple.Some new exact travelling wave solutions in more general form of these two nonlinear equations are derived by this extended method.The method introduced here appears to be easier and faster comparatively by means of symbolic computation system.
