  The spectrum of elementary excitations in one-dimensional quantum liquids is
generically linear at low momenta. It is characterized by the sound velocity
that can be related to the ground state energy. Here we study the spectrum at
higher momenta in Galilean invariant integrable models. Somewhat surprisingly,
we show that the spectrum at arbitrary momentum is fully determined by the
properties of the ground state. We find general exact relations for the
coefficients of several terms in the expansion of the excitation energy at low
momenta and arbitrary interaction and express them in terms of the Luttinger
liquid parameter. We apply the obtained formulas to the Lieb-Liniger model and
obtain several new results.
