Lump solutions and rogue waves in the generalized (3+1)-dimensional KP equation: reference frame dependence

In this paper, we study a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation. Using the Hirota bilinear method combined with successive traveling-wave transformations and dimensional reduction, we systematically derive a family of exact rational solutions, including 1-lump, 3-lump, and 6-lump wave solutions. A central and novel finding of this study is the reference frame dependent behavior of these lump solutions, when observed in a fixed spatial section (e.g., z = 0), they manifest as transient rogue waves that emerge abruptly from a constant background, attain a sharp peak, and subsequently vanish. In contrast, the same mathematical expressions, when viewed in a co-moving reference frame (e.g., along the line z = x), describe stable, shape preserving multi-soliton complexes that propagate with constant amplitude. This dual interpretation reveals an intrinsic unity between lump waves and line rogue waves, demonstrating that they represent different observational perspectives of the same underlying solution. Furthermore, we analyze the effects of dispersion parameters on the amplitude scaling and spatiotemporal structure of higher-order lump solutions. These results provide a unified framework for understanding extreme wave events in dissipative media and offer new insights into the geometric and kinematic aspects of nonlinear wave localization