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Setting Limits on Supersymmetry Using Simplified Models
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Published on: November 15, 2013

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Integrable discrete PT symmetric model.

Mark J Ablowitz1, Ziad H Musslimani2

  • 1Department of Applied Mathematics, University of Colorado, Campus Box 526, Boulder, Colorado 80309-0526, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2014
PubMed
Summary
This summary is machine-generated.

A new discrete nonlinear Schrödinger-like model with PT symmetry was developed. This exactly solvable model exhibits unique soliton behaviors like power oscillations and singularity formation.

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Area of Science:

  • Mathematical Physics
  • Nonlinear Dynamics
  • Quantum Mechanics

Background:

  • Nonlinear Schrödinger equations are fundamental in various fields.
  • PT-symmetric systems offer unique properties in physics.
  • Discrete models are crucial for numerical and theoretical studies.

Purpose of the Study:

  • Introduce a novel, exactly solvable discrete PT-invariant nonlinear Schrödinger-like model.
  • Investigate the properties of solitons within this new discrete framework.
  • Explore the connection to nonlocal nonlinear Schrödinger equations.

Main Methods:

  • Developed an integrable Hamiltonian system with nonlinear PT symmetry.
  • Employed a left-right Riemann-Hilbert formulation for solution construction.
  • Analyzed the behavior of the discrete one-soliton solution.

Main Results:

  • Successfully constructed a discrete one-soliton solution.
  • Observed unique soliton features including power oscillations.
  • Identified singularity formation in the discrete soliton.
  • Demonstrated the model as a discretization of a nonlocal nonlinear Schrödinger equation.

Conclusions:

  • The introduced discrete model is exactly solvable and PT-invariant.
  • The model exhibits novel soliton dynamics not seen in continuous counterparts.
  • This work provides a discrete platform for studying complex nonlinear phenomena.