Abstract
Using bifurcation method and numerical simulation approach of dynamical systems, we study a two-component Fornberg-Whitham equation. Two types of bounded traveling wave solutions are found, that is, the kink-like wave and compacton-like wave solutions. The planar graphs of these solutions are simulated by using software Mathematica; meanwhile, two new phenomena are revealed; that is, the periodic wave solution can become the kink-like wave or compacton-like wave solution under some conditions, respectively. Exact implicit or parameter expressions of these solutions are given.
Highlights
The Fornberg-Whitham equation ut − uxxt + ux + uux = uuxxx + 3uxuxx (1)was used to study the qualitative behaviors of wave breaking [1]
We have found two types of bounded traveling wave solutions for a two-component Fornberg-Whitham equation (see (4)), that is, the compacton-like wave and kinklike wave solutions
In different Cases i (i = 1– 16), the exact implicit or parameter expressions of kink-like wave and compacton-like wave solutions are given
Summary
Was used to study the qualitative behaviors of wave breaking [1]. It admits a wave of the greatest height, as a peaked limiting form of the traveling wave solution [2], u(x, t) = Ãexp((1/2)|x − (4/3)t|), where à is an arbitrary constant. 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. He et al [8] studied the following modified FornbergWhitham equation: ut − uxxt + ux + u2ux = uuxxx + 3uxuxx. They investigated the existence of the smooth and nonsmooth traveling wave solutions and gave some analytic expressions of smooth solitary wave, periodic cusp wave, and peakon solutions for (3). Was subjected to experimental and analytical studies They found certain solitary wave solutions which vanish identically outside a finite core region.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
