Abstract
Bright and dark solitons of the cubic nonlinear Schrödinger equation are used to construct complex-valued potentials with all-real spectrum. The real part of these potentials is equal to the intensity of a bright soliton, whereas their imaginary part is defined by the product of such soliton with its concomitant, a dark soliton. Considering light propagation in Kerr media, the real part of the potential refers to the self-focusing of the signal and the imaginary one provides the system with balanced gain-and-loss rates.
Original language | English |
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Pages (from-to) | 3381-3392 |
Number of pages | 12 |
Journal | Mathematical Methods in the Applied Sciences |
Volume | 45 |
Issue number | 7 |
DOIs | |
State | Published - 15 May 2022 |
Keywords
- Complex-valued potentials
- Darboux-transformation
- Gross-Pitaevskii Equation
- Optical Solitons
- PT-Symmetry
- Supersymmetric Quantum Mechanics