Quasi-classical soliton-type solutions of Hartry equations

Three-dimensional Hartry equations $ih\,\partial{\psi}/\partial{t}=-h^2\Delta\psi+U\psi$, $\Delta U=|\psi|^2$, are discussed. Asymptotic ($h\to0$) solutions $\psi$ of soliton type, localized $\operatorname{mod}0(h^\infty)$ in a compact domain are constructed. The corresponding asymptotics for the potential are obtained. Quantization conditions for the energy of the soliton are found.