Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example
Abstract
In the present work, we combine the notion of parity-time (PT) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power-law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which is absent for the corresponding solution of the regular nonlinear Schrödinger equation with arbitrary power-law nonlinearity. The spectral properties and dynamical implications of this instability are examined. Furthermore, we believe that these findings may pave the way toward initiating a fruitful interplay between the notions of PT symmetry, supersymmetric partner potentials, and nonlinear interactions.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. de Sevilla, Sevilla (Spain)
- Savitribai Phule Pune Univ., Pune (India)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1234658
- Alternate Identifier(s):
- OSTI ID: 1222513
- Report Number(s):
- LA-UR-15-25290
Journal ID: ISSN 1539-3755; PLEEE8
- Grant/Contract Number:
- IRSES-605096; NSF-DMS-1312856; 2010239; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
- Additional Journal Information:
- Journal Volume: 92; Journal Issue: 4; Journal ID: ISSN 1539-3755
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Kevrekidis, Panayotis G., Cuevas–Maraver, Jesús, Saxena, Avadh, Cooper, Fred, and Khare, Avinash. Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example. United States: N. p., 2015.
Web. doi:10.1103/PhysRevE.92.042901.
Kevrekidis, Panayotis G., Cuevas–Maraver, Jesús, Saxena, Avadh, Cooper, Fred, & Khare, Avinash. Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example. United States. https://doi.org/10.1103/PhysRevE.92.042901
Kevrekidis, Panayotis G., Cuevas–Maraver, Jesús, Saxena, Avadh, Cooper, Fred, and Khare, Avinash. Thu .
"Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example". United States. https://doi.org/10.1103/PhysRevE.92.042901. https://www.osti.gov/servlets/purl/1234658.
@article{osti_1234658,
title = {Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example},
author = {Kevrekidis, Panayotis G. and Cuevas–Maraver, Jesús and Saxena, Avadh and Cooper, Fred and Khare, Avinash},
abstractNote = {In the present work, we combine the notion of parity-time (PT) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power-law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which is absent for the corresponding solution of the regular nonlinear Schrödinger equation with arbitrary power-law nonlinearity. The spectral properties and dynamical implications of this instability are examined. Furthermore, we believe that these findings may pave the way toward initiating a fruitful interplay between the notions of PT symmetry, supersymmetric partner potentials, and nonlinear interactions.},
doi = {10.1103/PhysRevE.92.042901},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 4,
volume = 92,
place = {United States},
year = {Thu Oct 01 00:00:00 EDT 2015},
month = {Thu Oct 01 00:00:00 EDT 2015}
}
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