Travelling wave solutions of the Fornberg–Whitham equation

Bifurcations of traveling wave solutions for a two-component Fornberg–Whitham equation

“…We notice that if an orbit of (12) does not intersect with the singular line / = c, then, / 0 n is well defined in (11). It follows that this orbit defines a smooth solution on the (n, /) plane.…”

“…Possible traveling wave solutions of (1) were given in [11] and were classified in [12]. The modification of the Fornberg-Whitham equation was made.…”

Kink-Like Wave and Compacton-Like Wave Solutions for a Two-Component Fornberg-Whitham Equation

“…where , are two integral constants and ̸ = 0 (if = 0, then = 0 from the second equation of (7) and (6). In this case (4) reduces to (1), which was studied in [3][4][5][6][7]).…”

“…Feng and Wu [6] considered the classification of single traveling wave solutions to (1). Chen et al [7] gave some smooth periodic wave, smooth solitary wave, periodic cusp wave, and loopsoliton solutions of (1) and made the numerical simulation.…”

Numerical Investigation of Modified Fornberg Whitham Equation

“…Zhou and Tian, [16] have obtained kink-like wave solutions and antikink-like wave solutions of the equation by bifurcation method. Homotopy perturbation method (HPM) [7] reduced differential transform method [10], and phase portrait analytical technology [5] have been used to obtain exact and numerical solutions of Fornberg-Whitham equation. In [9], He et al investigated modified Fornberg Whitham equation and obtained some peakons and solitary waves of the equation.…”