Bilinear Bäcklund, Lax pairs, breather waves, lump waves and soliton interaction of (2+1)-dimensional non-autonomous Kadomtsev–Petviashvili equation

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

“…Some researchers have successfully constructed soliton solutions [16][17][18], lump solutions [19,20], interactional solutions [21][22][23][24][25], and other exact solutions [26] in different nonlinear systems. In [27], Ma first proposed a quadratic function method to construct lump solutions of a few generalized KP and BKP equations, and this kind of lump solutions can be localized in the whole plane.…”

The non-autonomous generalized perturbed KdV equation: its integrability, infinite conservation laws, multi soliton, high-order breather and hybrid solutions with mixed backgrounds

“…Naturally, damping rises in almost all real-world situations [28]- [35]. Also, there are so many physical situations where external excitation feels, for instance, plasma wave propagating in astronomical space environment moves under the influence of external periodic and hyperbolic forces in many cases [36]- [38]. For instance, for geophysical and marine purposes, waves produced by moving ships or flowing over the bottom topography need to be modeled using external forces [39,40].…”

“…Especially, Hirota's approach is a popular, efficient, and effective technique to find different complicated solutions of nonlinear partial differential equations viz., multi-soliton, breather, lump, rouge, and positon, etc. [35,38,58]. There are also many other techniques for deriving multisolitons.…”