A Three-wave Interaction Model With Self-consistent Sources:(?)-dressing Method And Solutions

In the paper, we study the three-wave interaction model with self-consistent sources and give its explicit solutions by virtue of the (?)-dressing method, which is based on the local3×3matrix (?)-problem. Using the properties of the (?)-problem and the Cauchy-Green operator, we derive the Lax pair and the associated evolution equation. Under suitable symmetry condition, we give the three-wave interaction model with self-consistent sources and its explicit Solutions, including one-soliton, two-soliton solution. In addition, on the basis of the three-wave interaction model with self-consistent sources, we obtain the gen-eration of second harmonics with self-consistent sources.