Exact solutions for a perturbed nonlinear Schrödinger equation by using Bäcklund transformations

Kink-like wave and compacton-like wave solutions for generalized KdV equation

“…(7), and the bounded integral curves of Eq. (7) correspond to the orbits of system (8) in which ϕ = ϕ(ξ ) is bounded. Therefore, we can simulate the bounded integral curves of Eq.…”

“…Therefore, we can simulate the bounded integral curves of Eq. (7) by using the information of the phase portraits of system (8).…”

“…It follows from [17][18][19][20][21] that the open orbits K i (i = 1, 2, 3, 4, 5, 6) of system (8) correspond to the compacton-like waves of Eq. (5), the heteroclinic orbits J i (i = 1, 2) of system (8) correspond to the kinklike waves of Eq.…”

“…(5), the heteroclinic orbits J i (i = 1, 2) of system (8) correspond to the kinklike waves of Eq. (5), the periodic orbits surrounding the center point (ϕ 2 , 0) correspond to the periodic waves of Eq.…”

“…The nonlinear evolution equations are playing important roles in the analysis of these phenomena. Many mathematical methods have been employed to find exact traveling wave solutions for these nonlinear evolution equations, such as Jacobi elliptic function method [1,2], F-expansion and extended F-expansion method [3,4], ( G G )-expansion method [5,6], Bäcklund transformation method [7,8], integral bifurcation method combined with factoring technique [9] and so on.…”