  We investigate transition of a one-dimensional interacting Bose gas from a
strongly repulsive regime to a strongly attractive regime, where a stable
highly excited state known as the super Tonks-Girardeau gas was experimentally
realized very recently. By solving exact dynamics of the integrable
Lieb-Liniger Bose gas, we demonstrate that such an excited gas state can be a
very stable dynamic state. Furthermore we calculate the breathing mode of the
super Tonks-Girardeau gas which is found to be in good agreement with
experimental observation. Our results show that the highly excited super
Tonks-Girardeau gas phase can be well understood from the fundamental theory of
the solvable Bose gas.
