Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation

Figure 2

Four low-kink waves are bifurcated from four symmetric solitary waves. The varying process for the figures of 𝑢^±_𝑎 and 𝑢^±_𝑏 when 𝜆>0, 𝜆≠𝛽²₁−4𝛼₁, (𝑎,𝑏)∈𝐴₂, and 𝑏→−(5𝑎²/48𝑐)+0, where 𝜆=50, 𝛾=𝛿=𝑐=𝑎=1, and (a) 𝑏=−(5𝑎²/48𝑐)+10⁻², (b) 𝑏=−(5𝑎²/48𝑐)+10⁻⁴, (c) 𝑏=−(5𝑎²/48𝑐)+10⁻⁶, and (d) 𝑏=−(5𝑎²/48𝑐)+10⁻⁹.

(a)

(b)

(c)

(d)