Article
Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example
Author/s | Kevrekidis, Panayotis G.
Cuevas-Maraver, Jesús ![]() ![]() ![]() ![]() ![]() ![]() ![]() Saxena, Avadh Cooper, Fred Khare, Avinash |
Department | Universidad de Sevilla. Departamento de Física Aplicada I |
Publication Date | 2015 |
Deposit Date | 2015-10-06 |
Published in |
|
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 P¨oschl-Teller ... 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 P¨oschl-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 Schr¨odinger equation with arbitrary power-law nonlinearity. The spectral properties and dynamical implications of this instability are examined. 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. |
Funding agencies | Department of Energy. United States |
Files | Size | Format | View | Description |
---|---|---|---|---|
PRE_Cuevas_2015_interplay.pdf | 1.108Mb | ![]() | View/ | |