Interplay between paritytime symmetry, supersymmetry, and nonlinearity: An analytically tractable case example
In the present work, we combine the notion of paritytime (PT) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the socalled PöschlTeller 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 powerlaw 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 powerlaw 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]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. de Sevilla, Sevilla (Spain)
 Savitribai Phule Pune Univ., Pune (India)
 Publication Date:
 Report Number(s):
 LAUR1525290
Journal ID: ISSN 15393755; PLEEE8
 Grant/Contract Number:
 IRSES605096; NSFDMS1312856; 2010239; AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)
 Additional Journal Information:
 Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print); Journal Volume: 92; Journal Issue: 4; Journal ID: ISSN 15393755
 Publisher:
 American Physical Society (APS)
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1234658
 Alternate Identifier(s):
 OSTI ID: 1222513
Kevrekidis, Panayotis G., Cuevas–Maraver, Jesús, Saxena, Avadh, Cooper, Fred, and Khare, Avinash. Interplay between paritytime symmetry, supersymmetry, and nonlinearity: An analytically tractable case example. United States: N. p.,
Web. doi:10.1103/PhysRevE.92.042901.
Kevrekidis, Panayotis G., Cuevas–Maraver, Jesús, Saxena, Avadh, Cooper, Fred, & Khare, Avinash. Interplay between paritytime symmetry, supersymmetry, and nonlinearity: An analytically tractable case example. United States. doi:10.1103/PhysRevE.92.042901.
Kevrekidis, Panayotis G., Cuevas–Maraver, Jesús, Saxena, Avadh, Cooper, Fred, and Khare, Avinash. 2015.
"Interplay between paritytime symmetry, supersymmetry, and nonlinearity: An analytically tractable case example". United States.
doi:10.1103/PhysRevE.92.042901. https://www.osti.gov/servlets/purl/1234658.
@article{osti_1234658,
title = {Interplay between paritytime 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 paritytime (PT) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the socalled PöschlTeller 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 powerlaw 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 powerlaw 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 (Print)},
number = 4,
volume = 92,
place = {United States},
year = {2015},
month = {10}
}