Abstract
We study the general lump-type soliton solutions on a background of periodic line waves in the PT-symmetric nonlocal Davey–Stewartson I (DS I) equation. By using the Kadomtsev–Petviashvili hierarchy reduction method, new families of semi-rational solutions termed as lump-soliton solutions to the nonlocal DS I equation are constructed. Under particular parameters restrictions we obtain: (a) different types of lumps sitting on a background of periodic line waves and (b) different types of lumps interacting with line solitons on a background of periodic line waves. The interactions of lumps and line solitons are inelastic, generating three generic dynamical scenarios: (i) lumps fusing into line solitons, (ii) lumps fissioning from line solitons, and (iii) a combined process consisting of lumps fusing into and fissioning from line solitons.
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