Wave propagation of resonance multi-stripes, complexitons, and lump and its variety interaction solutions to the (2+1)-dimensional pKP equation

Abstract

This study deals with the (2+1)-dimensional potential Kadomtsev-Petviashvili (pKP) equation, which is used to describe the dynamics of a wave of small but finite amplitude in two dimensions in diverse areas of physics and applied mathematics. Through symbolic computations with Maple, the resonance multi-stripe solutions in real fields, and multi-stripe complexiton solutions in complex fields are derived via the simplified linear superposition principle in conjunction with Hirota's bilinear method (HBM). Furthermore, lump, lump-stripe, and lump-triangular periodic wave solutions are derived by employing the HBM. A positive quadratic function with exponential, hyperbolic cosine and trigonometric cosine functions are considered to reach such aims. For lump solutions, it is found that the shape and amplitude of a lump wave remain unchanged during its propagation. On the other hand, lump-stripe interaction solitons present the fission and fusion interaction phenomena between the lump and stripe solitons. To illustrate the dynamical characteristics of the attained solutions, the three-dimensional (3D) and contour plots of some of the representative attained solutions are displayed with the particular choice of the free parameters. The obtained solutions and their physical features might be helpful to understand the propagation of small but finite amplitude waves in shallow water.