  Nonlinear Schr\"{o}dinger equations and corresponding quantum hydrodynamic
(QHD) equations are widely used in studying ultracold boson-fermion mixtures
and superconductors. In this article, we show that a more exact account of
interaction in Bose-Einstein condensate (BEC), in comparison with the
Gross-Pitaevskii (GP) approximation, leads to the existence of a new type of
solitons. We use a set of QHD equations in the third order by the interaction
radius (TOIR), which corresponds to the GP equation in a first order by the
interaction radius. The solution for the soliton in a form of expression for
the particle concentration is obtained analytically. The conditions of
existence of the soliton are studied. It is shown what solution exists if the
interaction between the particles is repulsive. Particle concentration of order
of $10^{12}$-$10^{14}$ $cm^{-3}$ has been achieved experimentally for the BEC,
the solution exists if the scattering length is of the order of 1 $\mu$m, which
can be reached using the Feshbach resonance. It is one of the limit case of
existence of new solution. The corresponding scattering length decrease with
the increasing of concentration of particles. The investigation of effects in
the TOIR approximation gives a more detail information on interaction
potentials between the atoms and can be used for a more detail investigation
into the potential structure.
