Gap solitons of a super-Tonks-Girardeau gas in a one-dimensional periodic potential

Motivated by the recent experimental realization of a super-Tonks-Girardeau (STG) gas (Haller et al 2009 Science 325 1224), we study in detail the existence and stability of gap solitons of the STG gas in a one-dimensional optical lattice. In particular, we explore the composition relationship of various gap solitons and nonlinear Bloch waves, taking into account the interplay between the periodic potential and the nonlinear interaction. The analysis of the linear stability indicates that unstable gap solitons can become stable by increasing the amplitude of the periodic potential or decreasing the nonlinear interaction. Moreover, it is found that due to the weak contribution of the interaction, gap solitons in a higher band gap (higher family) can easily form near the bottom of the linear Bloch band gaps in comparison with their counterparts in a lower band gap (lower family). Numerical calculations verify the validity of the composition relationship between various gap solitons and nonlinear Bloch waves in the STG phase. The results predicted for an STG gas confined by an optical lattice should be experimentally observable.