Fornberg–whitham equation

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August undefined, 2024

WebMar 29, 2024 · Fractional Fornberg-Whitham equation with He's fractional derivative is studied in a fractal process. The fractional complex transform is adopted to convert the studied fractional equation into a ... WebOct 6, 2024 · The numerical solution of the Fornberg–Whitham type equations (1) is numerically challenging. To solve these equations numerically, several methods were proposed in the literature. Lu in [33] solved Fornberg–Whitham type equations by He’s variational iteration method.

The Analytical Analysis of Time-Fractional Fornberg–Whitham …

WebMany mathematical properties of the Fornberg-Whitham equation have been dis-cussed, this equation was rst proposed for studying the qualitative behavior of wave breaking in … WebApr 1, 2024 · M. Ehrnström, J. Escher, and L. Pei, “ A note on the local well-posedness for the Whitham equation,” in Elliptic and Parabolic Equations, Proceedings in Mathematics and Statistics (Springer, 2015), Vol. 119, pp. 63– 75. Google Scholar Crossref; 6. J. M. Holmes, “ Well-posedness of the Fornberg–Whitham equation on the circle,” J. Differ library of things sacramento public library

On the analytical solution of Fornberg–Whitham equation with …

WebFeb 20, 2024 · The FW equation was compared with the famous Korteweg-de Vries (KdV) equation [ 23] \begin {aligned} u_t+6uu_x+u_ {xxx}=0, \end {aligned} and the classical Camassa-Holm (CH) equation [ 3, 4, 5, 6, 7, 8, 9, 11] \begin {aligned} u_t-u_ {xxt}+3uu_x=2u_xu_ {xx}+uu_ {xxx}. \end {aligned} WebJun 16, 2024 · This article is dealing with the analytical solution of Fornberg–Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate … WebDec 13, 2024 · The Fornberg-Whitham equation is shown to yield peakon solutions as a physical equation for waves of restricting height and the occurrences of wave breaking. Fractional calculus is now widely used and accepted, owing to its well-known uses in a variety of fields of seemingly disparate sectors of science and engineering [3, 4]. library of things smithtown

New Approximate Solutions to Time Fractional Order Partial

The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations

WebOct 1, 2011 · A generalization of the Fornberg–Whitham equation, that is, a two-component Fornberg–Whitham equation has been proposed for the first time. Employing the dynamical bifurcation method, we have studied the dynamical behavior and obtained three types traveling wave solutions of the two-component Fornberg–Whitham equation. library of things mordenIn mathematical physics, the Whitham equation is a non-local model for non-linear dispersive waves. The equation is notated as follows: This integro-differential equation for the oscillatory variable η(x,t) is named after Gerald Whitham who introduced it as a model to study breaking of non-linear dispersive water waves in 1967. Wav… library of trigonometric functions

"WebJan 11, 2024 · The solution of time-fractional Fornberg–Whitham equation is a topic for the researchers since long. Recently the analytical solution of time-fractional Fornberg–Whitham equation is the main focus of the researchers and mathematicians. This was the challenging work to extend or develop the existing techniques for the … " - Fornberg–whitham equation

Fornberg–whitham equation

WebApr 9, 2024 · In this article, a closed-form iterative analytic approximation to a class of nonlinear singularly perturbed parabolic partial differential equation is developed and analysed for convergence. We have considered both parabolic reaction diffusion and parabolic convection diffusion type of problems in this paper. The solution of this class of … WebIn mathematical physics, the Whitham equation is a non-local model for non-linear dispersive waves. [1][2][3] For faster navigation, ... The resulting integro-differential equation can be reduced to the partial differential equation known as the Fornberg–Whitham equation: ...

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WebJan 20, 2024 · In this paper, an analytical technique is proposed to determine the exact solution of fractional order modified Fornberg–Whitham equation. Since exact solution of fractional Fornberg–Whitham equation is unknown, first integral method has been applied to determine exact solutions. The solitary wave solution of fractional modified … WebJul 31, 2024 · In this article, modified techniques, namely the variational iteration transform and Shehu decomposition method, are implemented to achieve an approximate analytical solution for the time-fractional Fornberg–Whitham equation. A comparison is made between the results of the variational iteration transform method and the Shehu …

WebIn this paper, we investigate the wave breaking for the Fornberg-Whitham (FW) equation. Based on blow-up analysis of a Riccati-type inequality with a t-dependent function, which … WebJan 11, 2024 · The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method Authors: Nehad Ali Shah Sejong University...

WebJun 18, 2015 · Math.264, 65 (2014), analytical solution of space-time fractional Fornberg–Whitham equation is obtained in series form using the relatively new method called q-homotopy analysis method (q-HAM). The new fractional derivative makes it possible to introduce fractional order in space to the Fornberg–Whitham equation and be able … WebWe consider the Cauchy problem for the generalized Fornberg–Whitham equation with dissipation. This is one of the nonlinear, nonlocal and dispersive-dissipative equations. The main topic of this paper is an asymptotic analysis for the solutions to this problem. We prove that the solution to this

WebIn addition, when η = 1, Equation is reduced to the original Fornberg–Whitham equation, which was first proposed by Whitham in 1967 for studying the qualitative behavior of wave breaking . In 1978, Fornberg and Whitham [ 10 ] obtained a peaked solution of the form ψ ( χ , ζ ) = K e x p − 1 / 2 χ − 4 ζ / 3 , where K is an ...

WebJan 25, 2024 · We investigate the wave-breaking mechanism of solutions to a Fornberg-Whitham-type equation. By means of a weaker conserved L 2-norm, we show some wave-breaking criteria for the equation, which improve some blow-up results on the classical Fornberg-Whitham equation.Moreover, our conclusions suggest that the wave … library of trinity college dublinWebDec 15, 2024 · Classical Solutions of the Fornberg-Whitham Equation Georgia Burkhalter, Ryan C. Thompson, Madison Waldrep In this paper, we prove well-posedness in (a.k.a. … mci to charleston scWebMar 1, 2024 · A linear dispersive Fornberg–Whitham equation was investigated in where smooth and non-smooth travelling wave solutions were acquired. The global existence of … library of university of groningenWebA Numerical Approach of Fornberg-Whitham Equation Using Residual Power Series Method Abstract: In this paper, a modern and approach method called residual power … mci to grenada flightsWebDec 1, 2024 · This paper is devoted to studying wave breaking phenomena for the Fornberg–Whitham equation. Making use of the structure and the conservation quantity … mci to hawaii flightsWeb2011年，Lu J F[5]应用变分迭代法求解了Fornberg-Whitham方程，验证了此方法求解该方程的可靠性和有效性.2012年，李歆[6]介绍了变分迭代法求解中立型微分方程，从理论上证明该方法的收敛性。2013年，姜兆敏[7]利用变分迭代法得到常微分方程初值问题的无穷级数解 ... mci to brownsville txWebpendence) for the Fornberg-Whitham equation in both supercritical Besov spaces Bs p,r, s > 1+ 1 p, 1 ≤ p,r ≤ +∞ and critical Besov spaces B 1+1 p p,1, 1 ≤ p < +∞, which improves the previous work [20, 21, 36]. Then, we prove the solution is not uniformly continuous dependence on the initial data in supercritical Besov spaces Bs p,r, s ... library of up