Breather, lump, and interaction solutions to a nonlocal KP system

Abstract A new high-dimensional two-place Alice–Bob-Kadomtsev–Petviashvili (AB-KP) equation is proposed by applying the Alice–Bob-Bob–Alice principle and shifted-parity, delayed time reversal, charge conjugation ( P ˆ s T ˆ d C ˆ ) principle to the usual KP equation. Based on the dependent variable transformation, the bilinear form of the AB-KP system is constructed. Explicit trigonometric-hyperbolic, rational and rational-hyperbolic solutions are presented by taking advantage of the Hirota bilinear method. The obtained breather, lump, and interaction solutions enrich the solution structure of nonlocal nonlinear systems. The three-dimensional graphs of these nonlinear wave solutions are demonstrated by choosing the specific parameters.