Some Explicit Expressions and Interesting Bifurcation Phenomena for Nonlinear Waves in Generalized Zakharov Equations

Figure 8

(The four 2-blow-up waves become four 1-blow-up waves.) The varying process for the figures of 𝜑^±_𝑐 and 𝜑^±_𝑑 when (𝑞,𝑝)∈𝐴₃,𝜆<0,𝜆≠−𝜆₀/12, and 𝑝→3𝑞²/16𝑟−0, where 𝑟=1, 𝑞=−4,𝜆=−4,and𝑙₂∶𝑝=3𝑞²/16𝑟=3 and (a) 𝑝=3−10⁻¹, (b) 𝑝=3−10⁻³, (c) 𝑝=3−10⁻⁶, and (d) 𝑝=3−10⁻⁹.

(a)

(b)

(c)

(d)