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 2. The schematic diagram of the nonlinear superposition principles of two types of nonlinear waves of equation (1): (a) the breath wave; (b) the converted wave. In (a), the characteristic direction of the SWC is different from that of the PWC, and their characteristic lines are intersecting (${L}_{S}\nparallel {L}_{P}$). In (b), the characteristic direction of the SWC is the same as that of the PWC, and their characteristic lines are parallel to each other (${L}_{S}\parallel {L}_{P}$). ‘LS’ (red line) is the characteristic line of the SWC and ‘LP’ (blue line) is that of the PWC. Arrows of different colors represent the directions of characteristic lines for the corresponding wave components (SWC and PWC).