Fig 1.
(a) Phase portrait for system (5) for the values c0 = 1.2, c1 = −1, c2 = 1, c3 = 4.44541, D = 0, k = 1, α = 1, γ = 1, λ = 0.3, ϵ = 1, A = 0, and B = −1, (b) Profile of the solution according to the central point (Right-Blue point), and (c) Profile of the solution according to the central point (Origin-Red point).
Fig 2.
(a) Phase portrait for system (5) for the values c0 = 1.2, c1 = −1, c2 = 1, c3 = 4.44541, D = 1, k = 1, α = 1, γ = 1, λ = 0.3, ϵ = 1, A = 0, and B = −1, (b) Profile of the solution according to the central point (Right-Blue point), and (c) Profile of the solution according to the central point (Left-Red point).
Fig 3.
(a) Phase portrait for system (5) for c0 = 1.2, c1 = −2, c2 = 0.1, c3 = 0.941527, D = 1, k = 1, α = 1, γ = 1, λ = −0.1, ϵ = 1, A = 0, and B = −1, (b) Profile of the solution according to the saddle point (Right-Blue point), and (c) Profile of the solution according to the central point (Left-Red point).
Fig 4.
Phase portrait for system (17) for the parametric values c0 = 1, c1 = −0.2, c2 = 1, c3 = −1.61, α = 1, γ = 1, ε = 1, λ = 1, k = 1, D = 0.35 and (b) Profile of peakon solution for the same parametric values.
Fig 5.
Periodic peakon solution for the parametric values c0 = 1, c1 = −1.5, c2 = 1, c3 = 1.87316, α = 1, γ = 1, ε = 1, λ = 0.94, k = 1, D = 0.59 and (b) Profile of periodic peakon solution for the same parametric values.
Fig 6.
Profile of peakon solution (59) is plotted in the plane (x, t) for α = 1, γ = 0, ε = 1, c0 = c2 = 1, c1 = 3, c3 = 5c2, and η0 = 0.