Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example

Kevrekidis, Panayotis G.; Cuevas–Maraver, Jesús; Saxena, Avadh; Cooper, Fred; Khare, Avinash

doi:10.1103/PhysRevE.92.042901

Title: Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example

Journal Article · Thu Oct 01 00:00:00 EDT 2015 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.92.042901· OSTI ID:1234658

Kevrekidis, Panayotis G. ^[1]; Cuevas–Maraver, Jesús ^[2]; Saxena, Avadh ^[1]; Cooper, Fred ^[1]; Khare, Avinash ^[3]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. de Sevilla, Sevilla (Spain)
Savitribai Phule Pune Univ., Pune (India)

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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: IRSES-605096; NSF-DMS-1312856; 2010239; AC52-06NA25396

OSTI ID:: 1234658

Alternate ID(s):: OSTI ID: 1222513

Report Number(s):: LA-UR-15-25290; PLEEE8

Journal Information:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 92, Issue 4; ISSN 1539-3755

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 20 works

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Nonlinear switching and solitons in PT-symmetric photonic systems: Nonlinear PT-symmetric photonic systems Suchkov, Sergey V.; Sukhorukov, Andrey A.; Huang, Jiahao Laser & Photonics Reviews, Vol. 10, Issue 2 https://doi.org/10.1002/lpor.201500227	journal	February 2016
Complex PT-invariant cnoidal and hyperbolic solutions of several real nonlinear equations Khare, Avinash; Saxena, Avadh Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 17 https://doi.org/10.1088/1751-8121/aab4d8	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 Khare, Avinash; Cooper, Fred; Dawson, John F. Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 44 https://doi.org/10.1088/1751-8121/aae1cf	journal	October 2018
Supersymmetric laser arrays Hokmabadi, Mohammad P.; Nye, Nicholas S.; El-Ganainy, Ramy Science, Vol. 363, Issue 6427 https://doi.org/10.1126/science.aav5103	journal	February 2019
Phase-space quantum profile of Pöschl-Teller two-level systems Bernardini, A. E.; da Rocha, R. The European Physical Journal Plus, Vol. 134, Issue 1 https://doi.org/10.1140/epjp/i2019-12436-2	journal	January 2019
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Supersymmetric Laser Arrays Hokmabadi, Mohammad P.; Nye, Nicholas S.; El-Ganainy, Ramy CLEO: Science and Innovations, Conference on Lasers and Electro-Optics https://doi.org/10.1364/cleo_si.2019.sw4n.1	conference	January 2019
Exact solutions of a generalized variant of the derivative nonlinear Schrodinger equation in a Scarff II external potential and their stability properties Khare, Avinash; Cooper, Fred; Dawson, John F. arXiv https://doi.org/10.48550/arxiv.1805.04059	text	January 2018
Supersymmetric Laser Arrays Hokmabadi, Mohammad P.; Nye, Nicholas S.; El-Ganainy, Ramy arXiv https://doi.org/10.48550/arxiv.1812.10690	text	January 2018

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