Shape-changed propagations and interactions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluids

Dan-Dan Zhang,Lei Wang,Lei Liu,Tai-Xing Liu,Wen-Rong Sun

Figure 11. The classification of the converted waves (schematic diagram). ‘B’ = Bell-shaped wave, ‘W’ = W-shaped wave, ‘QB’ = Quasi Bell-shaped wave, ‘QW’ = Quasi W-shaped wave, ‘M’ = M-shaped wave, ‘OW’ =  Oscillating W-shaped wave, ‘OM’ = Oscillating M-shaped wave, ‘MPS’ = Multi-peak solitary wave, ‘QPW’ = Quasi periodic wave, ‘PW’ = Periodic wave. We introduce a function $\tau ={{\rm{e}}}^{-\delta }$ ($\tau \in [0,1]$, $\delta =| \tfrac{{a}_{1}}{{b}_{1}}| $). The closer to the left end point (point 0), the stronger the soliton state and the weaker the periodic state. On the contrary, the closer to the right end point (point 1), the weaker the soliton state and the stronger the periodic state. Except for the two endpoints, all other converted waves contain both soliton and periodic states.