Evolutionary higher-order lump–rogue waves in an integrable (3+1)-dimensional complex Kadomtsev–Petviashvili model: Insights on the dynamical patterns through explicit solutions

The rogue wave phenomenon continues to attract ever-increasing interest in both theoretical and experimental exploration, with higher-dimensional nonlinear soliton models possessing more fascinating evolutionary dynamics. This motivated the present work to study the evolutionary characteristics of lump–rogue waves in an integrable (3+1)-dimensional complex Kadomtsev–Petviashvili model with complex dispersion-nonlinearity coefficients by constructing explicit solutions through the Hirota bilinearization technique and generalized recursive polynomials. With systematic analysis of the solutions, we reveal the dynamical features and various pattern formation strategies of lump–rogue waves and provide extensive graphical demonstrations. The results are discussed elaborately with certain possible future directions. The observed results can be helpful for enhancing the understanding of localized nonlinear evolutionary waves. • An integrable (3+1)D complex-coefficient Kadomtsev–Petviashvili model is studied. • Higher-order lump–rogue wave solutions are constructed through bilinear formalism. • Evolutionary characteristics of lump–rogue waves are explored. • Effects of varying dispersion-nonlinearity are investigated in the lump–rogue waves. • Different pattern formation schemes of higher-order lump–rogue waves are revealed.