The Theoretical Study Of The Gap Solitons In Super-tonks-girardeau Gas

In2009year，with the Feshbach resonance technique developed，Haller et al. findthat there is a one-dimensional stable excited state by sudden turning the interaction fromstrongly repulsive to strongly attractive interaction. This cold atomic gas is called theSuper-Tonks-Girardeau(STG) gas.In this paper, we study the STG gas.First of all，we obtain the modified nonlinear Schr dinger equation of the STG gaswho has the strongly attractive interaction in one-dimensional by the density functionalmethod.We also obtain four GP equations of the Bose gas in one-dimensional with thestrongly repulsive, weakly repulsive, strongly attractive and weakly attractive limited.Secondly,we solve the time-dependent nonlinear Schr dinger equation by theimaginary time evolution method and find the chemical potential.Then，the gap solitons and nonlinear Bloch waves are obtained by solving them withthe Newton-relaxation method. With the gap solitons which we study, we find therelationship of the interaction, norm, chemical potential, and the order of gap solitons.Then, we test the composition relation in the strongly attractive still right.At last, the linear stability analysis indicates that the unstable gap solitons canbecome stable by decreasing the nonlinear interaction. It is found that the gap solitons inthe higher-band gap (higher-family) are easy to form near the bottom of the linear Blochband gaps, which is due to the weak interaction in comparison with their counterparts inthe lower-band gap (lower-family).