title: Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example.
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 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. 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.affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA and Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Panayotis G
authors.initials: PG
authors.lastname: Kevrekidis
authors.affiliation: Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla. Escuela Politécnica Superior, C/ Virgen de África, 7, 41011-Sevilla, Spain and Instituto de Matemáticas de la Universidad de Sevilla (IMUS). Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012-Sevilla, Spain.
authors.forename: Jesús
authors.initials: J
authors.lastname: Cuevas-Maraver
authors.affiliation: Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Avadh
authors.initials: A
authors.lastname: Saxena
authors.affiliation: Santa Fe Institute, Santa Fe, New Mexico 87501, USA and Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Fred
authors.initials: F
authors.lastname: Cooper
authors.affiliation: Physics Department, Savitribai Phule Pune University, Pune 411007, India.
authors.forename: Avinash
authors.initials: A
authors.lastname: Khare