  In an effort to address integrability breaking in cold gas experiments, we
extend the integrable hydrodynamics of the 1d Lieb-Liniger model with two
additional components representing the population of atoms in the first and
second transverse excited states, thus enabling a description of quasi-1d
condensates. Collisions between different components are accounted for through
the inclusion of a Boltzmann-type collision integral in the hydrodynamic
equation. Contrary to standard generalized hydrodynamics, our extended model
captures thermalization of the condensate at a rate consistent with
experimental observations from a quantum Newton's cradle setup.
