Abstract
The Kadomtsev-Petviashvili (KP) equation is instrumental in characterizing nonlinear wave phenomena in fluid dynamics. With the incorporation of three-dimensional disturbances, the (3+1)-dimensional KP equation emerges. In this study, we employ the Hirota bilinear method to investigate a (3+1)-dimensional KP equation. We successfully derive both lump and lump-chain solutions for this equation. The characteristics of the resulting lump are thoroughly examined. It is observed that those lumps propagate along a specific ray direction, with the origin of these rays dependent on the imaginary part of σˆjk=σj−σk with 1≤j,k≤3 and j≠k. We have simultaneously obtained the propagation direction of these rays. The periodicity of those lumps is denoted as Tjk dependent on spectrum parameter. Furthermore, we explore two potential lines, including the characteristic line associated with the lumps, to gain a deeper understanding of the nonlinear waves controlled by this system.
Published Version
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