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

Figure 8

(The anti-kink wave is bifurcated from the bell-shape solitary wave). The varying process for the graph of 𝑢_𝑒 when 𝑐>0, 𝛿>0, 𝑎>0, 𝜆>0 and 𝑏→−16𝑎²/75𝑐+0. Where 𝑐=1, 𝛿=1, 𝑎=1, 𝜆=50 and (a) 𝑏=−16𝑎²/75𝑐+10⁻¹. (b) 𝑏=−16𝑎²/75𝑐+10⁻³. (c) 𝑏=−16𝑎²/75𝑐+10⁻⁴. (d) 𝑏=−16𝑎²/75𝑐+10⁻⁷.

(a)

(b)

(c)

(d)