New Types of Nonlinear Waves and Bifurcation Phenomena in Schamel-Korteweg-de Vries Equation

Figure 9

(The kink wave is bifurcated from the blow-up wave). The varying process for the graph of 𝑢_𝑑 when 𝑐>0, 𝛿>0, 𝑎>0, 𝜆>0, and 𝑏→−16𝑎²/75𝑐−0, where 𝑐=1, 𝛿=1, 𝑎=1, 𝜆=1, and (a) 𝑏=−16𝑎²/75𝑐−10⁻². (b) 𝑏=−16𝑎²/75𝑐−10⁻⁴. (c) 𝑏=−16𝑎²/75𝑐−10⁻⁵. (d) 𝑏=−16𝑎²/75𝑐−10⁻⁹.

(a)

(b)

(c)

(d)