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One-dimensional quantum fluids are usually described within the Luttinger liquid theory. It simplifies a real system by replacing the true energy-momentum relation for its particles with a linear one. Including the spectrum nonlinearity has proven to be difficult. The talk reviews recent breakthrough in theory of a non-linearized fluid. The nonlinear Luttinger liquid theory (term coined by Adilet Imambekov) predicts a set of new universal singularities of the dynamic response functions and an emergence of kinetics, absent in the linear Luttinger liquid. The new theory is a generalization of the original one, and is applicable to a diverse group of systems. These include, for example, electrons in quantum wires and cold atomic gases in one-dimensional traps.
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