Theory of one-dimensional Bose gas with point interaction

The first three terms in the asymptotics of the solution of the Lieb–Lieniger equation in the exact theory of one-dimensional Bose-gas with point interaction are founds in the analytical form in the weak coupling limit. The asymptotical formulas for the energy density, particle number density and pressure coincide with the corresponding formulas obtained in the framework of perturbation theory in the hydrodynamical action method, which is based on continual integral.