Compacton and generalized kink wave solutions of the CH–DP equation

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

“…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.…”

“…Substituting (20) into dϕ/dξ = y and integrating along J + 1 and J − 1 for initial value ϕ(0) = ϕ * 1 , where 0 < ϕ * 1 < ϕ 3 , we obtain two kinklike wave solutions of implicit expression as follows…”

“…They found certain solitary wave solutions which vanish identically outside a finite core region. These solutions are called compactons, and several studies have been conducted in [16][17][18][19][20][21]. The kink-like wave or generalized kink wave was discovered by Liu [17], which is defined on semifinal bounded domain and possesses some properties of the kink wave.…”

Exact traveling wave solutions of a KPI equation

“…Sinelshchikov [3] demonstrate that four solutions from 13 of the KPI obtained by Khalfallah [2] are wrong and do not satisfy the equation. In this paper, we employ the method of dynamical systems [4][5][6][7] to investigate the traveling waves of the KPI.…”

Periodic and solitary travelling-wave solutions of a CH–DP equation

“…In recent years, the CH-DP equation has been widely studied by many authors [10][11][12][13][14][15][16][17][18][19][20]. Xie and Wang [20] obtained exact explicit parameter expressions of compactons and implicit expressions of generalized kink wave solutions of Eq.…”