A variational solution to fundamental solitons in superlattices

Abstract

A variational technique is established to study the fundamental solitons in a superlattice’s potential. The variational results show that the fundamental solitons can only exit in the semi-infinite gap and there exists a critical propagation constant of fundamental solitons, below which the solitons vanish. The value of is associated with the edge of the first band. Following numerical simulations, the variational results are in good agreement with the numerical results.