Bifurcations and Parametric Representations of Peakon, Solitary Wave and Smooth Periodic Wave Solutions for a Two-Component Degasperis-Procesi Equation

Figure 1

The graphics of the function 𝑓(𝜙) when 𝑐≠0. (a) 𝑐<0,  𝑘<0. (b) 𝑐<0, 0<𝑘<𝑘_∗. (c) 𝑐<0, 𝑘=𝑘_∗. (d): 𝑐<0, 𝑘>𝑘_∗. (e) 𝑐>0, 𝑘<0. (f) 𝑐>0, 0<𝑘<𝑘_∗. (g) 𝑐>0, 𝑘=𝑘_∗. (h) 𝑐>0, 𝑘>𝑘_∗.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)