Bifurcation Analysis and Different Kinds of Exact Travelling Wave Solutions of a Generalized Two-Component Hunter-Saxton System

Figure 1

Bifurcation sets and phase portraits of system (10).

(a) 𝑐<0,𝐴<4𝑐

(b) 𝑐<0,𝐴=4𝑐

(c) 𝑐<0,4𝑐<𝐴<0

(d) 𝑐<0,𝐴=0

(e) 𝑐<0,0<𝐴<−(1/2)𝑐

(f) 𝑐<0,𝐴=−(1/2)𝑐

(g) 𝑐<0,𝐴>−(1/2)𝑐

(h) 𝑐>0,𝐴<−(1/2)𝑐

(i) 𝑐>0,𝐴=−(1/2)𝑐

(j) 𝑐>0,−(1/2)𝑐<𝐴<0

(k) 𝑐>0,𝐴=0

(l) 𝑐>0,0<𝐴<4𝑐

(m) 𝑐>0,𝐴=4𝑐

(n) 𝑐>0,𝐴>4𝑐