Gap solitons in almost periodic one-dimensional structures
Analysis of PDEs
2015-02-04 v3 Mathematical Physics
math.MP
Abstract
We consider almost periodic stationary nonlinear Schr\"odinger equations in dimension . 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.
Cite
@article{arxiv.1410.3287,
title = {Gap solitons in almost periodic one-dimensional structures},
author = {Alexander Pankov},
journal= {arXiv preprint arXiv:1410.3287},
year = {2015}
}