[en] One- and two-soliton solutions of the scalar nonlinear Schroedinger equation with self-consistent potentials of the Yajima-Oikawa type were found and investigated, by using the algebraic-geometric integration method of the nonlinear differential equations. The obtained solitons, in analogy with SG breathers have binding energies. The values of binding energies were calculated for the given spectral data. The investigation shows that the scalar nonlinear Schroedinger equation with the given self-consistent potentials has both one- and two-soliton regular solutions. (author)