Abstract
In this letter, we obtain families of semi-rational solutions termed lump-soliton solutions to the Fokas system by using the Hirota's bilinear method combined with the Kadomtsev–Petviashvili (KP) hierarchy reduction method. These exact semi-rational solutions illustrate the collision of lumps and dark-line solitons. Two different types of evolution scenarios occur: (a) fusion of lumps and dark-line solitons into dark-line solitons, and (b) fission of dark-line solitons into lumps and dark-line solitons. In these distinct evolution processes, the lumps would get either created or annihilated by the dark-line solitons.
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