  We study the stability of gap solitons of the super-Tonks-Girardeau bosonic
gas in one-dimensional periodic potential. The linear stability analysis
indicates that increasing the amplitude of periodic potential or decreasing the
nonlinear interactions, the unstable gap solitons can become stable. In
particular, the theoretical analysis and numerical calculations show that,
comparing to the lower-family of gap solitons, the higher-family of gap
solitons are easy to form near the bottoms of the linear Bloch band gaps. The
numerical results also verify that the composition relations between various
gap solitons and nonlinear Bloch waves are general and can exist in the
super-Tonks-Girardeau phase.
