Fornberg–whitham equation

Author: jwcf

August undefined, 2024

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 … 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: ...

The generalized time-fractional Fornberg–Whitham equation: An …

WebSep 24, 2024 · In this article, we investigate the Fornberg–Whitham (FW) equation V_ {t}-V_ {txx}-V_ {x}+\frac {3} {2}VV_ {x}= \frac {9} {2}V_ {x}V_ {xx}+\frac {3} {2}VV_ {xxx}, (1) … Webthe Fornberg-Whitham equation to the two-component system. Unlike the CH system (equa-tion) or DP system (equation), they possess inﬁnitely many conserved quantities, a Lax pair terry spear book list in order

Wave breaking to a shallow water wave equation involving the Fornberg …

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 … 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 … Webpendence) 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 ... trillmatic lyrics

The Variational Iteration Transform Method for Solving the Time

Dissipative and conservative local discontinuous …

WebMar 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 … 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. terry speaksWebJun 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 … terry spear author

"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 … " - Fornberg–whitham equation

Fornberg–whitham equation

Wave breaking to a shallow water wave equation involving the Fornberg …

WebOct 5, 2024 · We consider the Cauchy problem for the Fornberg–Whitham (FW) equation(1.1){uxxt−ut+92uxuxx+32uuxxx−32uux+ux=0u(x,0)=u0(x),when x∈Ror Tand t∈R. This equation was first written down in 1967 by Whitham [41]and again by Whitham and Fornberg [19]as a model for breaking waves. WebOct 5, 2024 · In this paper, we consider the wave breaking for the Fornberg–Whitham (FW) equation (1) { u t − u x x t + 3 2 u u x − 9 2 u x u x x − 3 2 u u x x x − u x = 0, t > 0, x ∈ …

Did you know?

WebDec 1, 2009 · FW equation has a wave of greatest height peaked at the crest and admits the solution u (x, t) = 8 9 exp − 1 2 x − 4 3 t in the limiting form, where is a parameter (Fornberg and Whitham... 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

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 ... Web2011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 ...

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 … WebA Numerical Approach of Fornberg-Whitham Equation Using Residual Power Series Method Abstract: In this paper, a modern and approach method called residual power …

WebDec 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 …

WebDec 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. … trillmatic hatWebNov 26, 2016 · Fornberg and Whitham obtained a peaked solution of the form u ( x , t ) = Ae −1/2 ( x−4t/3 ) where A is an arbitrary constant. Preliminaries and notations In this section, we set up notation and review some basic definitions from fractional calculus [ 14, 15 ]. Definition 2.1 terry spear booksWebModifications of the Optimal Auxiliary Function Method to Fractional Order Fornberg-Whitham Equations. 2024-02-17 Hakeem Ullah Mehreen Fiza Ilyas Khan Abd Allah Mosa Saeed Islam and Abdullah Mohammed. ... (OAFM) for fractional-order equations using the Caputo operator, which is named FOAFM.The mathematical theory of FOAFM is … trillogy piercing oaklandWebWe 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 trillo fan lightIn 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… trill nightclubWebMar 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 ... terry spear dawn of the jaguarWebK fw ( s) = 1 2 ν e − ν s and c fw = ν 2 ν 2 + k 2, with α fw = 3 2. The resulting integro-differential equation can be reduced to the partial differential equation known as the Fornberg–Whitham equation: [6] ( ∂ 2 ∂ x 2 − ν 2) ( ∂ η ∂ t + 3 2 η ∂ η ∂ x) + ∂ η ∂ x = 0. trillogy inhalant powder.com