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Stability analysis of multiple solutions of nonlinear Schrödinger equation with \(\mathbf {\mathcal{PT}\mathcal{}}\)-symmetric potential

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Abstract

Exact stationary solutions of nonlinear Schrödinger equation in the presence of complex deformed supersymmetric potential have been obtained in terms of bright soliton and dark soliton. As an example, \(\mathcal{PT}\mathcal{}\)-symmetric Scarf potential has been considered. Then the corresponding spectrum of linear Schrödinger equation has been investigated, and the \(\mathcal{PT}\mathcal{}\) broken and unbroken regions of linear Schrödinger equation have been delineated analytically. The bright soliton and a bright-dark soliton solutions of the nonlinear Schrödinger equation are retrieved analytically with real eigenvalues. Moreover, the stability of these solutions is corroborated by means of linear stability analysis which are validated by direct numerical simulations in terms of a wide range of potential amplitudes for focusing as well as defocusing cases. Finally, we illustrate the strength of stability of bright and dark solitons through the adiabatic transformations on system parameters. Then connected and disconnected stable regions of bright and dark solitons are examined.

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Acknowledgements

DN dedicates this article to the memory of his kind brother, late Raj Kumar Nath. AD gratefully acknowledges financial support from SERB-DST, Govt. of India (EEQ/2017/000150), and DST PURSE-II University of Kalyani.

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  1. Department of Mathematics, University of Kalyani, Kalyani, WB, 741235, India

    Niladri Ghosh & Amiya Das

  2. Department of Mathematics, Vivekananda College, Kolkata, WB, 700063, India

    Debraj Nath

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  1. Niladri Ghosh
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Ghosh, N., Das, A. & Nath, D. Stability analysis of multiple solutions of nonlinear Schrödinger equation with \(\mathbf {\mathcal{PT}\mathcal{}}\)-symmetric potential. Nonlinear Dyn 111, 1589–1605 (2023). https://doi.org/10.1007/s11071-022-07900-x

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