The D'Alembert type waves and the soliton molecules in a (2+1)-dimensional Kadomtsev-Petviashvili with its hierarchy equation*

Hui-Ling Wu(吴慧伶),Sheng-Wan Fan(樊盛婉),Jin-Xi Fei(费金喜),Zheng-Yi Ma(马正义)

Figure 6. (a) The soliton molecule expressed a line soliton and the breather for the variable v of equation (17) with the condition equations (55)–(58) at t = 0. (b) The soliton molecule constructed the line soliton molecule and the breather for the variable v of equation (17) with the condition equations (61) and (62) at t = 0. (c) The elastic interaction between the line soliton molecule and the breather with the condition equations (61) and (63) at t = 0. (d) The soliton molecule formed through two breathers with the condition equations (68) and (69) at t = 0.