This paper focuses upon the derivation of the exact solutions for a nonlinear physical system arising in fluid dynamic problem. Starting from a special Painlevé-Bäcklund transformation with a trivial seed solution and using a multilinear variable separation approach, an exact variable separation solution to the (2+1)-dimensional Kadomtsev-Petviashvili (KP) system is derived. Then, based on the derived exact solution, we reveal some significant localized excitations including drimions, peakons, compactons, foldons and chaotic patterns in the (2+1)-dimensional KP system by prescribing appropriate boundary conditions and/or initial conditions.
v