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

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:
OSTI Identifier:
1234658
Report Number(s):
LA-UR--15-25290
Journal ID: ISSN 1539-3755; PLEEE8
Grant/Contract Number:
IRSES-605096; NSF-DMS-1312856; 2010239; AC52-06NA25396
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 1539-3755
Publisher:
American Physical Society (APS)
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING