Two-layer fluid formation and propagation of periodic solitons induced by (3+1)-dimensional KP equation

In this paper, multi-wave solutions of Kadomtsev–Petviashvili KP equation with time variable coefficient are obtained. It is found that the formation of two-layer with bright and dark soliton which are symmetric. These solitons are transversely periodic as periodic of two-soliton and two-antisoliton in time with cusps localized in space. These two types of waves propagate in an opposite direction relative the higher layer. the autonomous behavior may be argued to the fact that the KP is composed of the derivative and the anti-derivative terms.