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

Figure 2

The simulations of integral curves of (8) when 𝜃=−1, 𝑔=−1.39361 (corresponding to Example 1), and 𝑔=−0.696804 (corresponding to Example 2). (a) 𝜑(0)=1 and 𝜑^′(0)=−0.5160826789900144. (b) 𝜑(0)=1 and 𝜑^′(0)=0.5160826789900144. (c) 𝜑(0)=−1 and 𝜑^′(0)=−1.1707040231039854. (d) 𝜑(0)=−1 and 𝜑^′(0)=1.1707040231039854. (e) 𝜑(0)=1 and 𝜑^′(0)=0. (f) 𝜑(0)=−1.624378546433569 and 𝜑^′(0)=0.

(a)

(b)

(c)

(d)

(e)

(f)