Non-Linear Stationary Solutions in Realistic Models for Analog Black-Hole Lasers
Abstract
:1. Introduction
2. Gravitational Analogues in Bose–Einstein Condensates
2.1. Effective One-Dimensional Configurations
2.2. Gross–Pitaevskii and Bogoliubov—De Gennes Equations
2.3. Analog Configurations
2.4. Solutions of the Homogeneous Gross—Pitaevskii Equation
3. General Relation between Black Holes and Black-Hole Lasers
4. Attractive Square Well
4.1. General Structure
4.2. Homogeneous Plane Wave
4.3. Asymptotic Shadow Solitons
4.4. Asymptotic Solitons
4.4.1. Symmetric Solutions
Incomplete-Soliton Solutions
Complete-Soliton Solutions
4.4.2. Asymmetric Solutions
5. Double Delta-Barrier
5.1. General Structure
5.2. Symmetric Solutions
5.2.1. Solutions
5.2.2. Solutions
5.2.3. Solutions
5.3. Asymmetric Solutions
5.3.1. Solutions
5.3.2. Solutions
6. Conclusions and Outlook
Acknowledgments
Conflicts of Interest
Appendix A. Elliptic Functions
Appendix B. Computation of the Non-Linear Solutions of the Attractive Square Well
Appendix B.1. Homogeneous Plane Wave
Appendix B.2. Subsonic Shadow Solitons
Appendix B.3. Subsonic Solitons
Appendix B.3.1. Symmetric Solutions
Incomplete-Soliton Solutions
Complete-Soliton Solutions
Appendix B.3.2. Asymmetric Solutions
Appendix C. Computation of the Non-Linear Solutions of the Double Delta-Barrier
Appendix C.1. Symmetric Solutions
Appendix C.1.1. S+ Solutions
Appendix C.1.2. S− Solutions
Appendix C.1.3. SD Solutions
Appendix C.2. Asymmetric Solutions
Appendix C.2.1. AC Solutions
Appendix C.2.2. AD Solutions
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De Nova, J.R.M. Non-Linear Stationary Solutions in Realistic Models for Analog Black-Hole Lasers. Universe 2017, 3, 54. https://doi.org/10.3390/universe3030054
De Nova JRM. Non-Linear Stationary Solutions in Realistic Models for Analog Black-Hole Lasers. Universe. 2017; 3(3):54. https://doi.org/10.3390/universe3030054
Chicago/Turabian StyleDe Nova, Juan Ramón Muñoz. 2017. "Non-Linear Stationary Solutions in Realistic Models for Analog Black-Hole Lasers" Universe 3, no. 3: 54. https://doi.org/10.3390/universe3030054