Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation

Figure 8

The orbits of system (2.5) connecting with the saddle points. (a) 0<𝑔<𝑔₁(𝑐),𝑐>𝛾; (b) 0<𝑔<𝑔₁(𝑐),𝑐<𝛾; (c) 𝑔=0,𝑐>𝛾; (d) 𝑔=0,𝑐<𝛾; (e) 𝑔₂(𝑐)<𝑔<0,𝑐>𝛾; (f) 𝑔₂(𝑐)<𝑔<0,𝑐<𝛾.

(a)

(b)

(c)

(d)

(e)

(f)