A three-wave interaction model with self-consistent sources: The ∂¯-dressing method and solutions

Abstract In the paper, we study the three-wave interaction model with self-consistent sources by virtue of the ∂ ¯ -dressing method. The explicit solutions, including one-soliton, two-soliton solution are obtained. In addition, on the basis of the three-wave interaction model with self-consistent sources, we obtain the generation of second harmonics with self-consistent sources.