Composition Relation between Gap Solitons and Bloch Waves in Nonlinear Periodic Systems

We show with numerical computation and analysis that Bloch waves, at either the center or edge of the Brillouin zone, of a one dimensional nonlinear periodic system can be regarded as infinite chains composed of fundamental gap solitons (FGSs). This composition relation between Bloch waves and FGSs leads us to predict that there are n families of FGSs in the nth band gap of the corresponding linear periodic system, which is confirmed numerically. Furthermore, this composition relation can be extended to construct a class of solutions similar to Bloch waves but with multiple periods.