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