Broken and unbroken \(\varvec{\mathcal {PT}}\)-symmetric solutions of semi-discrete nonlocal nonlinear Schrödinger equation

  • Y. HanifEmail author
  • U. Saleem
Original paper


In this letter, we obtain multi-soliton solutions in terms of ratio of ordinary determinants for semi-discrete nonlocal nonlinear Schrödinger (sd-NNLS) equation by employing the Darboux transformation. We construct explicit expressions of single and double soliton solutions in zero background. We obtain symmetry-broken and symmetry-unbroken soliton solutions of sd-NNLS equation by using appropriate eigenfunctions. We notice that for symmetry non-preserving case, the potential term exhibits stable structure whereas individual fields display instability. We also obtain blowup or oscillating singular-type soliton solutions for symmetry-preserving case.


Reverse space \(\mathcal {PT}\)-symmetry Semi-discrete nonlinear Schrödinger equation Darboux transformation Multi-soliton solutions Exceptional points 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no potential conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of the PunjabLahorePakistan

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