Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation

TL;DR

This paper explores the universal behavior of cold atomic gases in the weak nonlinearity, dispersion, and dissipation limit by mapping complex hydrodynamic models to well-known one-dimensional equations, aiding understanding of nonlinear wave dynamics.

Contribution

It introduces a reductive perturbation method to connect cold atom hydrodynamics with classical integrable equations, providing new insights into their interplay.

Findings

Mapping of hydrodynamic models to KdV, Burgers, and Benjamin-Ono equations

Estimates for original hydrodynamic equations derived from known solutions

Enhanced understanding of nonlinear wave propagation in cold atomic gases

Abstract

Dynamics of interacting cold atomic gases have recently become a focus of both experimental and theoretical studies. Often cold atom systems show hydrodynamic behavior and support the propagation of nonlinear dispersive waves. Although this propagation depends on many details of the system, a great insight can be obtained in the rather universal limit of weak nonlinearity, dispersion and dissipation (WNDD). In this limit, using a reductive perturbation method we map some of the hydrodynamic models relevant to cold atoms to well known chiral one-dimensional equations such as KdV, Burgers, KdV-Burgers, and Benjamin-Ono equations. These equations have been thoroughly studied in literature. The mapping gives us a simple way to make estimates for original hydrodynamic equations and to study the interplay between nonlinearity, dissipation and dispersion which are the hallmarks of nonlinear hydrodynamics.