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

Figure 9

The peakon is bifurcated from the singular cusp wave and the solitary wave. The varying process for the figures of 𝑣₁₁(𝜉) and 𝑣₁₂(𝜉) when 𝛼₁<0, 𝛽<0, and 𝛾→𝛾₂(𝛽)−0 where 𝛼₁=−2 and 𝛽=−9.

(a) 𝛾=𝛾₂(𝛽)−10⁻¹

(b) 𝛾=𝛾₂(𝛽)−10⁻⁴

(c) 𝛾=𝛾₂(𝛽)−10⁻⁸

(d) 𝛾=𝛾₂(𝛽)−10⁻¹

(e) 𝛾=𝛾₂(𝛽)−10⁻⁴

(f) 𝛾=𝛾₂(𝛽)−10⁻⁸