Gap solitons in almost periodic one-dimensional structures

作者：Pankov Alexander^*

来源：Calculus of Variations and Partial Differential Equations, 2015, 54(2): 1963-1984.

DOI：10.1007/s00526-015-0851-0

We consider almost periodic stationary nonlinear Schrodinger equations in dimension 1. Under certain assumptions we prove the existence of nontrivial finite energy solutions in the strongly indefinite case. The proof is based on a carefull analysis of the energy functional restricted to the so-called generalized Nehari manifold, and the existence and fine properties of special Palais-Smale sequences. As an application, we show that certain one dimensional almost periodic photonic crystals possess gap solitons for all prohibited frequencies.

• 出版日期2015-10