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

Figure 2

The 3-D graphs of profiles of the singular double-soliton solution (53) for parameters: (a) ℎ₀=0.15, 𝑐₀=1.5, 𝛼=0.2, 𝜆₁=−1, 𝜆₂=−0.2, 𝑟₁=−8.0, 𝑟₂=2.0, and 𝑎=0.1; (b) ℎ₀=3, 𝑐₀=−1.5, 𝛼=0.2, 𝜆₁=1, 𝜆₂=0.2, 𝑟₁=8, 𝑟₂=2.0, and 𝑎=−2.

(a)  0<ℎ₀<0.2,𝜆₁<0,𝜆₂<0

(b) ℎ₀>1,𝜆₁>0,𝜆₂>0