Periodic breather waves, stripe-solitons and interaction solutions for the (3+1)-dimensional variable-coefficient Kadomtsev–Petviashvili-like equation

The Kadomtsev–Petviashvili (KP) equation is a key model for weakly nonlinear dispersive waves, helping to understand wave behavior in complex systems like ion-acoustic waves in plasma and fluid dynamics. This work presents the (3+1)-dimensional Kadomtsev–Petviashvili-like (KP-like) equation with variable coefficients, concentrating on its novel localized waves and interaction solutions. The investigation begins by applying the superposition principle to the bilinear form of the equation to construct positive complexiton solutions up to the third order. Additionally, the Hirota bilinear method and ansatz function scheme are used to construct the exact solutions exhibit N-solitons, lump waves, breather waves and intriguing interactions such as lump-periodic waves, lump-rogue waves. Also, we extract the two cross-stripe solitons, two parallel stripe solitons, x-periodic breather, y-periodic breather and (x,y)-periodic breather waves, each representing different wave characteristics. To demonstrate and highlight the physical significance of the dynamics, we present solutions in 3D and contour plots with careful selected values of the free parameters. The originality of this work stems from the fact that these results, particularly for the equation with variable coefficients, have not been previously examined. This work provides a benchmark analysis of the KP equation, offering new perspectives on soliton dynamics and interactions with variable coefficients.