A New Discrete Integrable System Derived from a Generalized Ablowitz-Ladik Hierarchy and Its Darboux Transformation

Figure 5

The solutions of 𝑝_𝑛,𝑟_𝑛̃ in (3.13) show a shape of discrete kink or antikink soliton for fixed parametric values. Take (a) and (c) parameters as 𝜆₁=1,𝜆₂=2,𝛾₁=−0.5,𝛾₂=0.6, and take (a) and (c) parameters as 𝜆₁=−1,𝜆₂=0.9,𝛾₁=−0.5,𝛾₂=−0.6.

(a) 𝑡=0.2,𝑛∈[−20,20]

(b) 𝑡=0.2,𝑛∈[−40,40]

(c) 𝑡=0.2,𝑛∈[−20,20]

(d) 𝑡=0.2,𝑛∈[−40,40]