Explicit peakon and solitary wave solutions for the modified Fornberg–Whitham equation

He, Bin; Meng, Qing; Shao-Lin, LI

doi:10.1016/j.amc.2010.06.055

Cited by 28 publications

(15 citation statements)

References 22 publications

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“…In this paper, we apply the bifurcation method of dynamical systems [12][13][14][15][16][17][18][19][20][21][22][23] and the improved sub-ODE method [24][25][26][27][28][29][30] with the help of symbolic computation Mathematica and Maple to study solitary wave solutions of (1).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Bifurcation and Solitary-Like Solutions for Compound KdV-Burgers-Type Equation

Yin

Wei

Guo-ming

2015

Discrete Dynamics in Nature and Society

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Firstly, based on the improved sub-ODE method and the bifurcation method of dynamical systems, we investigate the bifurcation of solitary waves in the compound KdV-Burgers-type equation. Secondly, numbers of solitary patterns solutions are given for each parameter condition and numerical simulations are used to display the dynamical characteristics. Finally, we obtain twelve solitary patterns solutions under some parameter conditions, such as the trigonometric function solutions and the hyperbolic function solutions.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Bifurcation and Solitary-Like Solutions for Compound KdV-Burgers-Type Equation

Yin

Wei

Guo-ming

2015

Discrete Dynamics in Nature and Society

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“…Let us consider the Fornberg-Whitham equation given by [9] u t − u xxt + u x + uu x = 3u x u xx + uu xxx , t > 0, x > 0, (1.1) and first proposed by Whitham in 1967 for studying the qualitative behavior of wave breaking. In 1978, Fornberg and Whitham [6] obtained a peaked solution consisting of an arbitrary constant.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Modified Fornberg Whitham Equation

Yağmurlu

Yildiz

Uçar

et al. 2021

Mathematical Sciences and Applications E-Notes

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The aim of this study is to obtain numerical solutions of the modified Fornberg Whitham equation via collocation finite element method combined with operator splitting method. The splitting method is used to convert the original equation into two sub equations including linear and nonlinear part of the equation as a slight modification of splitting idea. After splitting progress, collocation method is used to reduce the sub equations into algebraic equation systems. For this purpose, quintic B-spline base functions are used as a polynomial approximation for the solution. The effectiveness and efficiency of the method and accuracy of the results are measured with the error norms L 2 and L ∞. The presentations of the numerical results are shown by graphics as well.

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“…Various methods such as the bifurcation theory and the method of phase portraits analysis [1], reduced differential transform method [4], and variational iteration method [5] have been developed independently for the solution of modified Fornberg-Whitham equation. But according to the best possible information of the authors, the detailed study of the nonlinear fractional order modified Fornberg-Whitham equation is only beginning.…”

Section: Introductionmentioning

confidence: 99%