Lump and Mixed Rogue-Soliton Solutions of the (2+1)-Dimensional Mel'nikov System

Lump wave and line rogue wave of the (2 + 1)-dimensional Mel'nikov system are derived by taking the ansatz as the rational function. By combining a rational function and different exponential functions, mixed solutions between the lump and soliton are derived. These solutions describe the interaction phenomena of the lump-bright soliton with fission and fusion, the half-line rogue wave with a bright soliton, and a rogue wave excited from the bright soliton pair, respectively. Some special concrete interaction solutions are depicted in both analytical and graphical ways.