Quasi-periodic structures and solitary wave interactions for the (3+1) Kadomtsev–Petviashvili-like equation under variable coefficients

Based on the extended homoclinic test method combining with breather period limit approach, we determine the general structure of breather-kink waves, rogue waves and double-solitary waves for the (Formula: see text)-dimensional Kadomtsev–Petviashvili-like (KP-like) equation under variable coefficients, which describes weakly nonlinear dispersive wave propagation. The influence of variable coefficients on nonlinear wave dynamics was examined through analytical and graphical analyses. The results emphasize that coefficient modulation plays a crucial role in controlling soliton shape, amplitude and energy distribution. Moreover, chaotic dynamics of the perturbed system is examined with two forms of perturbations: trigonometric function and Gaussian function and predicted through chaos detecting tools. Our findings are innovative and valuable in gaining a better understanding of nonlinear mechanisms in fluid dynamics, optics and mathematical physics.