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

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Abstract

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.

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  1. Department of Physics, University of the Punjab, Quaid-e-Azam Campus, Lahore, 54590, Pakistan

    Y. Hanif & U. Saleem

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  1. Y. Hanif
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  2. U. Saleem
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Hanif, Y., Saleem, U. Broken and unbroken \(\varvec{\mathcal {PT}}\)-symmetric solutions of semi-discrete nonlocal nonlinear Schrödinger equation. Nonlinear Dyn 98, 233–244 (2019). https://doi.org/10.1007/s11071-019-05185-1

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