Title: Exact form of the Bogoliubov excitations in one-dimensional nonlinear Schrödinger equation

Abstract: In the paper we present the exact solutions of one-dimensional Nonlinear Schr\"{o}dinger Equation. The solutions correspond to the Bogoliubov excitations in Bose-gas with a local interaction. The obtained expression is used for evaluating the transmission coefficient of the excitations across a delta-functional potential barrier.