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

Figure 1

The solitary wave is bifurcated from two types of periodic waves. The varying process for the figures of 𝑣₁(𝜉) and 𝑣₂(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