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

Figure 11

(The kink wave is bifurcated from the valley-shape solitary wave). The varying process for the graph of 𝑢_𝑓 when 𝑐>0, 𝛿>0, 𝑎>0, and 𝑏→−16𝑎²/75𝑐−0, where 𝑐=1, 𝛿=1, 𝑎=1/2, and (a) 𝑏=−16𝑎²/75𝑐−10⁻³. (b) 𝑏=−16𝑎²/75𝑐−10⁻⁷. (c) 𝑏=−16𝑎²/75𝑐−10⁻⁸. (d) 𝑏=−16𝑎²/75𝑐−10⁻¹⁰.

(a)

(b)

(c)

(d)