Periodic and Solitary Wave Solutions of Two Component Zakharov–Yajima–Oikawa System, Using Madelung's Approach

Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov–Yajima–Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions.