Fig. 1
(a) The 3D plot of u3.1 (ξ) when λ = 5, μ = 0.01, C1 = −5, C2 = −11, β = 6, γ = 1, k1 = 1; k2 = −1 and , showcasing it as a multi-soliton solution, (b) The 3D plot of v3.1 (ξ)) when λ = 3, , C1 = 2, C2 = 3, β = 11, γ = −3, k1 = 1; k2 = 2, and α = 1, showcasing it as a bright soliton solution.
Fig. 2
(a) The 3D plot of u3.2 (ξ) when λ = 0.1, μ = 1, C1 = −5, C2 = −11, β = 63, γ = 1, k1 = 1; k2 = −1 and , showcasing it as a kink wave solution, (b) The 3D plot of v3.2 (ξ) when λ = 0.3, μ = 111, C1 = 3, C2 = 2, β = −2, γ = −1, k1 = 1, k2 = 1, and , showcasing it as a multi-soliton solution.
Fig. 3
(a) The 3D plot of u3.3 (ξ) when λ = 4, μ = 4, C1 = −3, C2 = −5, β = 3, γ = 3, k1 = 3, k2 = 3 and α = 1, showcasing it as a solitary wave. (b) The 3D plot of v3.3 (ξ) when λ = 2, μ = 1, C1 = 1.1, C2 = 2, β = 15, γ = −1, k1 = 2, k2 = −2 and , showcasing it as a single wave behavior.
Fig. 4
(a) The 3D plot of h2.1 (ξ) when λ = 4, , β0 = 2, α2 = 2, C1 = −1, C2 = 1, p = 8, q = 2 and , showcasing it as multi-soliton solution, (b) The 3D plot of g2.1 (ξ)) when λ = 2, μ = 0.1, β0 = 1, α2 = 1, C1 = 4, C2 = 2, p = 6, q = 0.05 and , showcasing it as a soliton solution.
Fig. 5
(a) The 3D plot of h2.2 (ξ) when λ = 2, μ = 8, , β0 = 1, α2 = 2, C1 = −5, C2 = −11, p = 6 and q = 3, showcasing it as multi-soliton solution, (b) The 3D plot of g2.2 (ξ) when λ = 1, μ = 4, β0 = 2, α2 = 1, C1 = −11, C2 = 2, p = −4, q = 3 and , showcasing it as multi-soliton solution.
Fig. 6
(a) The 3D plot of of h3.3 (ξ) when λ = 2, μ = 1, , β0 = 1, α2 = 1, C1 = 1, C2 = 1, p = 6 and q = 5, showcasing it as Singular Kink wave solution, (b) The 3D plot of g3.3 (ξ) when λ = 2, μ = 1, β0 = 1, α2 = 1, C1 = 111, C2 = 5, p = 2, q = 5 and , showcasing it as singular anti Kink wave solution of
Fig. 7
(a) The 3D plot of ψ1.1 (ξ) when λ = 2, μ = 0.2, C1 = −5, C2 = 11, β = 1, k1 = 1 and , showcasing it as Singular Kink wave solution, (b) The 3D plot of ϕ1.1 (ξ)) when λ = 2, μ = 0.2, C1 = −1, C2 = 1, β = 1, k1 = 1, δ = 2, and , showcasing it as multi-soliton solution.
Fig. 8
(a) The 3D plot of ψ1.2 (ξ) when λ = 2, μ = 0.2, C1 = −5, C2 = 11, β = 1, k1 = 1 and , showcasing it as muli-soliton solution, (b) The 3D plot of ϕ1.2 (ξ) when λ = 1, μ = 4, C1 = −11, C2 = 2, β = 1, k1 = 1, δ = −4, and , showcasing it as multi-soliton solution.
Fig. 9
(a) The 3D plot of ψ1.3 (ξ)) when λ = 2, μ = 0.2, C1 = −5, C2 = 11, β = 1, k1 = 1 and , showcasing it as soliton solution, (b)The 3D plot of ϕ1.3 (ξ)) when λ = 2, μ = 1, C1 = 2, C2 = −2, β = −2, k1 = 2, δ = 2, and , showcasing it as soliton solution.