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

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