New Lax Pairs and Darboux Transformation and Its Application to a Shallow Water Wave Model of Generalized KdV Type

Figure 1

The 3-D graphs of profiles of the singular double-soliton solution (53) for fixed parameters 𝑐₀=1.5, 𝛼=0.2, 𝜆₁=−1, 𝜆₂=−0.2, 𝑟₁=−8.0, 𝑟2=2.0, and 𝑎=0.1.

(a) 0.3<ℎ₀<0.5,𝜆₁<0,𝜆₂<0

(b) 0.2<ℎ₀<0.3,𝜆₁<0,𝜆₂<0