  One-dimensional quantum fluids are conventionally described by using an
effective hydrodynamic approach known as Luttinger liquid theory. As the
principal simplification, a generic spectrum of the constituent particles is
replaced by a linear one, which leads to a linear hydrodynamic theory. We show
that to describe the measurable dynamic response functions one needs to take
into account the nonlinearity of the generic spectrum and thus of the resulting
quantum hydrodynamic theory. This nonlinearity leads, for example, to a
qualitative change in the behavior of the spectral function. The universal
theory developed in this article is applicable to a wide class of
one-dimensional fermionic, bosonic, and spin systems.
