Breather Waves, Periodic Cross-Lump Waves and Complexiton Type Solutions for the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation in Dispersive Media

The manuscript under consideration explores the (2+1)-dimensional Kadomtsev-Petviashvili (KP) model using its bilinear representation. The focus is on studying the characteristics of periodic cross-lump waves and breather wave solutions. Breathers, which are localized periodic solutions of continuous media equations or discrete lattice equations, are of particular interest. The research also delves into complexiton solutions using the extended transformed rational function approach. The study graphically analyzes the dynamics of these interaction solutions using appropriate parameters. It's truly fascinating to learn about the application of breathers in continuous media equations or discrete lattice equations.