Topologically protected edge gap solitons of interacting Bosons in one-dimensional superlattices<xref rid="cpb_27_6_060307_fn1" ref-type="fn">*</xref> <fn id="cpb_27_6_060307_fn1"> <label>*</label> <p>Project supported by the Natural Science Foundation of Hebei Province, China (Grant Nos. A2012203174 and A2015203387) and the National Natural Science Foundation of China (Grant Nos. 10974169 and 11304270).</p> </fn>

Topologically protected edge gap solitons of interacting Bosons in one-dimensional superlattices* *

Project supported by the Natural Science Foundation of Hebei Province, China (Grant Nos. A2012203174 and A2015203387) and the National Natural Science Foundation of China (Grant Nos. 10974169 and 11304270).

Guo Xi-Hua, Xu Tian-Fu^†, Liu Cheng-Shi^‡

(color online) (a) The linear Bloch energy bands (black solid lines) and the nonlinear Bloch energy bands (blue dashed lines) of the nonlinear Bloch Schrödinger equation (2). (b) The eigenvalues of the nonlinear Schrödinger equation (1) in ascending order under open boundary condition. The energy levels form three energy bands. One edge state appears in the first band gap and the other edge state appears in the second band gap. Their wave functions are plotted in Fig. 2 as blue solid lines.