In this article we prove the existence of a new family of periodic solutions for discrete, nonlinear Schrödinger equations subject to spatially localized driving and damping. They provide an alternate description of the metastable behavior in such lattice systems which agrees with previous predictions for the evolution of metastable states while providing more accurate approximations to these states. We analyze the stability of these breathers, finding a very small positive eigenvalue whose eigenvector lies almost tangent to the surface of the cylinder formed by the family of breathers. This causes solutions to slide along the cylinder without leaving its neighborhood for very long times.
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Special Section: 18th International Conference on II-VI Compounds and Related Materials Guest Editors: Xinyi Liu and Aidong Shen
Preface and peer reviewed journal articles of some of the topics that were to be presented at the Conference.
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- Award ID(s):
- 1723075
- PAR ID:
- 10087171
- Date Published:
- Journal Name:
- Journal of electronic materials
- Volume:
- 47
- Issue:
- 8
- ISSN:
- 0361-5235
- Page Range / eLocation ID:
- 4211 - 4411
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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