Coherent structures of lump-soliton for the PT-symmetric nonlocal Davey-Stewartson III equation on a background of constant or periodic line waves

The coherent structures of lump-soliton for the PT-symmetric nonlocal Davey-Stewartson III equation on the background of a constant or periodic line waves, described by two families of semi-rational solutions in terms of \(2N\times 2N\) $2N\times 2N$ or \((2N+1)\times (2N+1)\) $(2N+1)\times (2N+1)$ determinants respectively, are investigated by employing the Kadomtsev-Petviashvili (KP) hierarchy reduction method in conjunction with the Hirota’s bilinear technique. The waveforms and dynamical behaviors of the coherent structures of lump-soliton are discussed by graphical and analytical ways. In these coherent structures, the lumps would fuse into or detach from the line solitons. Particularly, under suitable parameter restrictions, the soltions would disappear, and the coherent structures of lump-soliton reduce to lumps on the background of a constant or periodic line waves.