Gap solitons of a super-Tonks-Girardeau gas in a one-dimensional   periodic potential
  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. 
T. F. Xu, X. L. Jing, H. G. Luo and C. S. Liu
cond-mat.quant-gas