Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System

Figure 2

The solitary wave is bifurcated from two types of periodic waves. The varying process for the figures of 𝑣₃(𝜉) and 𝑣₄(𝜉) when 𝛼₂>0, 𝛽<0, and 𝛾→𝛾₁(𝛽)−0 where 𝛼₂=4 and 𝛽=−9.

(a) 𝛾=𝛾₁(𝛽)−10⁻¹

(b) 𝛾=𝛾₁(𝛽)−10⁻⁴

(c) 𝛾=𝛾₁(𝛽)−10⁻⁸

(d) 𝛾=𝛾₁(𝛽)−10⁻¹

(e) 𝛾=𝛾₁(𝛽)−10⁻⁴

(f) 𝛾=𝛾₁(𝛽)−10⁻⁸