  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.
