Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $$\mathcal{PT}$$- and supersymmetric potential
Abstract
In this work, we present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex $$\mathcal{PT}$$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.
- Authors:
-
[1];
[2];
[3];
[5]
- California Polytechnic State Univ., San Luis Obispo, CA (United States)
- Univ. of New Hampshire, Durham, NH (United States)
- The Santa Fe Inst., NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
- Savitribai Phule Pune Univ., Pune (India)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1840878
- Report Number(s):
- LA-UR-20-22820
Journal ID: ISSN 1751-8113
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Physics. A, Mathematical and Theoretical
- Additional Journal Information:
- Journal Volume: 53; Journal Issue: 45; Journal ID: ISSN 1751-8113
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Charalampidis, Efstathios G., Dawson, John F., Cooper, Fred, Khare, Avinash, and Saxena, Avadh. Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential. United States: N. p., 2020.
Web. doi:10.1088/1751-8121/abb278.
Charalampidis, Efstathios G., Dawson, John F., Cooper, Fred, Khare, Avinash, & Saxena, Avadh. Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential. United States. https://doi.org/10.1088/1751-8121/abb278
Charalampidis, Efstathios G., Dawson, John F., Cooper, Fred, Khare, Avinash, and Saxena, Avadh. Wed .
"Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential". United States. https://doi.org/10.1088/1751-8121/abb278. https://www.osti.gov/servlets/purl/1840878.
@article{osti_1840878,
title = {Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential},
author = {Charalampidis, Efstathios G. and Dawson, John F. and Cooper, Fred and Khare, Avinash and Saxena, Avadh},
abstractNote = {In this work, we present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.},
doi = {10.1088/1751-8121/abb278},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 45,
volume = 53,
place = {United States},
year = {Wed Oct 28 00:00:00 EDT 2020},
month = {Wed Oct 28 00:00:00 EDT 2020}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Observation of PT phase transition in a simple mechanical system
journal, March 2013
- Bender, Carl M.; Berntson, Bjorn K.; Parker, David
- American Journal of Physics, Vol. 81, Issue 3
sl(2, ) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
journal, September 2000
- Bagchi, B.; Quesne, C.
- Physics Letters A, Vol. 273, Issue 5-6
Dynamic localization and transport in complex crystals
journal, December 2009
- Longhi, S.
- Physical Review B, Vol. 80, Issue 23
Observation of -Symmetry Breaking in Complex Optical Potentials
journal, August 2009
- Guo, A.; Salamo, G. J.; Duchesne, D.
- Physical Review Letters, Vol. 103, Issue 9
$\mathcal{PT}$ -Symmetric Periodic Optical Potentials
journal, February 2011
- Makris, K. G.; El-Ganainy, R.; Christodoulides, D. N.
- International Journal of Theoretical Physics, Vol. 50, Issue 4
$\mathcal{PT}$-symmetric electronics
journal, October 2012
- Schindler, J.; Lin, Z.; Lee, J. M.
- Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 44
Supersymmetry-generated one-way-invisible -symmetric optical crystals
journal, March 2014
- Midya, Bikashkali
- Physical Review A, Vol. 89, Issue 3
Supersymmetry in the fractional quantum Hall regime
journal, May 2017
- Sagi, Eran; Santos, Raul A.
- Physical Review B, Vol. 95, Issue 20
Observation of parity–time symmetry in optics
journal, January 2010
- Rüter, Christian E.; Makris, Konstantinos G.; El-Ganainy, Ramy
- Nature Physics, Vol. 6, Issue 3
Bloch Oscillations in Complex Crystals with Symmetry
journal, September 2009
- Longhi, S.
- Physical Review Letters, Vol. 103, Issue 12
Spectral singularities and Bragg scattering in complex crystals
journal, February 2010
- Longhi, S.
- Physical Review A, Vol. 81, Issue 2
Generating Complex Potentials with real Eigenvalues in Supersymmetric Quantum Mechanics
journal, June 2001
- Bagchi, B.; Mallik, S.; Quesne, C.
- International Journal of Modern Physics A, Vol. 16, Issue 16
-symmetry in honeycomb photonic lattices
journal, August 2011
- Szameit, Alexander; Rechtsman, Mikael C.; Bahat-Treidel, Omri
- Physical Review A, Vol. 84, Issue 2
Feast Eigensolver for Non-Hermitian Problems
journal, January 2016
- Kestyn, James; Polizzi, Eric; Peter Tang, Ping Tak
- SIAM Journal on Scientific Computing, Vol. 38, Issue 5
Parity–time synthetic photonic lattices
journal, August 2012
- Regensburger, Alois; Bersch, Christoph; Miri, Mohammad-Ali
- Nature, Vol. 488, Issue 7410
Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex -invariant potential
journal, April 2001
- Ahmed, Zafar
- Physics Letters A, Vol. 282, Issue 6
Parity–time-symmetric whispering-gallery microcavities
journal, April 2014
- Peng, Bo; Özdemir, Şahin Kaya; Lei, Fuchuan
- Nature Physics, Vol. 10, Issue 5
Solitons in coupled nonlinear Schrödinger models: A survey of recent developments
journal, November 2016
- Kevrekidis, P. G.; Frantzeskakis, D. J.
- Reviews in Physics, Vol. 1
The Physics of Non-Hermitian Operators
journal, July 2006
- Geyer, Hendrik; Heiss, Dieter; Znojil, Miloslav
- Journal of Physics A: Mathematical and General, Vol. 39, Issue 32
Beam Dynamics in Symmetric Optical Lattices
journal, March 2008
- Makris, K. G.; El-Ganainy, R.; Christodoulides, D. N.
- Physical Review Letters, Vol. 100, Issue 10
Making sense of non-Hermitian Hamiltonians
journal, May 2007
- Bender, Carl M.
- Reports on Progress in Physics, Vol. 70, Issue 6
Supersymmetric Optical Structures
journal, June 2013
- Miri, Mohammad-Ali; Heinrich, Matthias; El-Ganainy, Ramy
- Physical Review Letters, Vol. 110, Issue 23
Spectral singularities of odd- -symmetric potentials
journal, January 2019
- Konotop, Vladimir V.; Zezyulin, Dmitry A.
- Physical Review A, Vol. 99, Issue 1
Supersymmetric mode converters
journal, April 2014
- Heinrich, Matthias; Miri, Mohammad-Ali; Stützer, Simon
- Nature Communications, Vol. 5, Issue 1
Visualization of Branch Points in -Symmetric Waveguides
journal, August 2008
- Klaiman, Shachar; Günther, Uwe; Moiseyev, Nimrod
- Physical Review Letters, Vol. 101, Issue 8
Experimental study of active LRC circuits with symmetries
journal, October 2011
- Schindler, Joseph; Li, Ang; Zheng, Mei C.
- Physical Review A, Vol. 84, Issue 4
Physical realization of -symmetric potential scattering in a planar slab waveguide
journal, February 2005
- Ruschhaupt, A.; Delgado, F.; Muga, J. G.
- Journal of Physics A: Mathematical and General, Vol. 38, Issue 9
sl(2, ) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
journal, September 2000
- Bagchi, B.; Quesne, C.
- Physics Letters A, Vol. 273, Issue 5-6
PT-symmetry in honeycomb photonic lattices
text, January 2011
- Szameit, Alexander; Rechtsman, Mikael C.; Bahat-Treidel, Omri
- arXiv
Supersymmetric Optical Structures
text, January 2013
- Miri, Mohammad-Ali; Heinrich, Matthias; El-Ganainy, Ramy
- arXiv