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Continuous and discrete Schrödinger systems with parity-time-symmetric nonlinearities
Amarendra K Sarma1, Mohammad-Ali Miri2, Ziad H Musslimani3
1Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
Summary
Parity-time (PT) nonlinear Schrödinger equations exhibit unique soliton behaviors, differing from standard models. A discrete PT-nonlinear system is shown to be integrable, with nonlinearity dictating symmetry breaking.
Area of Science:
- Nonlinear optics
- Quantum mechanics
- Mathematical physics
Background:
- Nonlinear Schrödinger equations (NLSE) are fundamental in describing wave propagation.
- Parity-time (PT) symmetry offers new possibilities for Hamiltonian systems.
- Investigating PT-symmetric NLSE extends understanding of nonlinear dynamics.
Purpose of the Study:
- To explore the dynamical behavior of continuous and discrete PT-invariant nonlinear Schrödinger systems.
- To compare the behavior of PT-symmetric NLSE with standard NLSE counterparts.
- To analyze the integrability and symmetry-breaking conditions of a discrete PT-nonlinear system.
Main Methods:
- Analysis of continuous PT-symmetric nonlinear Schrödinger equations.
- Discretization of PT-nonlinear Schrödinger equations on a lattice.
- Derivation of invariants for the discrete system.
- Identification of PT-symmetry-breaking conditions.
Main Results:
- PT-symmetric NLSE can support both bright and dark soliton solutions simultaneously.
- A two-element discrete PT-nonlinear system is fully integrable.
- Exceptional points in this discrete system are determined by the nonlinearity.
- PT-symmetry-breaking conditions were identified.
Conclusions:
- PT-symmetric nonlinear systems exhibit distinct dynamical behaviors compared to standard NLSE.
- The discrete PT-nonlinear system offers a unique, integrable model.
- Nonlinearity plays a crucial role in dictating symmetry breaking and exceptional points.
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