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Title: 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:
 [1];  [2];  [1];  [1];  [3]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. de Sevilla, Sevilla (Spain)
  3. 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:
Journal Article: 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. 2015. "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},
url = {https://www.osti.gov/biblio/1234658}, journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
issn = {1539-3755},
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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Cited by: 20 works
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Works referencing / citing this record:

Nonlinear switching and solitons in PT-symmetric photonic systems: Nonlinear PT-symmetric photonic systems
journal, February 2016


Complex PT-invariant cnoidal and hyperbolic solutions of several real nonlinear equations
journal, April 2018


Exact solutions of a generalized variant of the derivative nonlinear Schrödinger equation in a Scarff II external potential and their stability properties
journal, October 2018


Supersymmetric laser arrays
journal, February 2019


Phase-space quantum profile of Pöschl-Teller two-level systems
journal, January 2019


Supersymmetric laser arrays
journal, September 2015


Supersymmetric Laser Arrays
conference, January 2019


Supersymmetric Laser Arrays
text, January 2018