Traveling Wave Solutions of the Benjamin-Bona-Mahony Water Wave Equations

Seadawy, Aly R.; Sayed, Aya

doi:10.1155/2014/926838

Cited by 20 publications

(8 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Two problems have been solved with different initial conditions. In [40], the authors have derived the Benjamin-Bona-Mahony and KdV equations from water wave model. Further travelling wave equations of these models have been derived by two different methods.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions

Kamran

Abbas

Majeed

et al. 2022

Journal of Function Spaces

View full text Add to dashboard Cite

The unidirectional propagation of long waves in certain nonlinear dispersive system is explained by the Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The purpose of this study is to investigate the BBM-Burger equation numerically using Caputo derivative and B-spline basis functions. The fractional derivative is considered in Caputo form, and L 1 formula is used for discretization of temporal derivative. The interpolation of space derivative is done with the help of B-spline functions. The effect of α and time on solution profile of travelling wave for different domain of x is discussed in this paper. The numerical results have been presented to show that the cubic B-spline method is effective and efficient in solving the time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. Moreover, the convergence and stability of the proposed scheme are analyzed. The error norms are also calculated to check the accuracy of the proposed scheme. The numerical results reflect that the proposed scheme can be used for linear and highly nonlinear models.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions

Kamran

Abbas

Majeed

et al. 2022

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

“…Nevertheless, the analysis of nonlinear equations involving arbitrary functions is often difficult and laborious. In particular, for dealing with the determination of exact solutions, several direct methods have been elaborated, among them Kudryashov method [5][6][7][8], tanh-sech method [9,10], Painlevé analysis [11,12], Adomian decomposition method [13][14][15][16] and other special methods [17,18]. However, these methods just work for a limited kind of equations.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions

2021

View full text Add to dashboard Cite

The Benjamin–Bona–Mahony equation describes the unidirectional propagation of small-amplitude long waves on the surface of water in a channel. In this paper, we consider a family of generalized Benjamin–Bona–Mahony–Burgers equations depending on three arbitrary constants and an arbitrary function G(u). We study this family from the standpoint of the theory of symmetry reductions of partial differential equations. Firstly, we obtain the Lie point symmetries admitted by the considered family. Moreover, taking into account the admitted point symmetries, we perform symmetry reductions. In particular, for G′(u)≠0, we construct an optimal system of one-dimensional subalgebras for each maximal Lie algebra and deduce the corresponding (1+1)-dimensional nonlinear third-order partial differential equations. Then, we apply Kudryashov’s method to look for exact solutions of the nonlinear differential equation. We also determine line soliton solutions of the family of equations in a particular case. Lastly, through the multipliers method, we have constructed low-order conservation laws admitted by the family of equations.

show abstract

“…The general projective Riccati equation method, Exp-function method, extended hyperbolic function method and collocation method with the modified exponential cubic B-spline have been applied to the third-order KdV equation [25][26][27][28]. Time-fractional generalized third-order KdV equation with modified Riemann-Liouville derivative has been solved by using generalized Kudryashov method [29].…”

Section: Introductionmentioning

confidence: 99%

SITEM for the Conformable Space-Time Fractional (2+1)-Dimensional Breaking Soliton, Third-Order KdV and Burger's Equations

Yaslan

2021

Mathematical Sciences and Applications E-Notes

View full text Add to dashboard Cite

In the present paper, new analytical solutions for the conformable space-time fractional (2+1)-dimensional breaking soliton, third-order KdV and Burger's equations are obtained by using the simplified tan( φ(ξ)2 )expansion method (SITEM). Here, fractional derivatives are described in conformable sense. The obtained traveling wave solutions are expressed by the trigonometric, hyperbolic, exponential and rational functions. Simulation of the obtained solutions are given at the end of the paper.

show abstract

Traveling Wave Solutions of the Benjamin-Bona-Mahony Water Wave Equations

Cited by 20 publications

References 26 publications

Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions

Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions

Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions

SITEM for the Conformable Space-Time Fractional (2+1)-Dimensional Breaking Soliton, Third-Order KdV and Burger's Equations

Contact Info

Product

Resources

About