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Dynamics of exact solutions of nonlinear resonant Schrödinger equation utilizing conformable derivatives and stability analysis

  • Regular Article – Nonlinear Dynamics
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Abstract

In this paper, we consider the conformable resonant nonlinear Schrödinger equation (CRNLSE) incorporating Kerr law nonlinearity and provide some new analytical solutions. Three analytical methods such as the Exp-function method, modified \(\exp (-\Phi (\eta ))\)-expansion function method, and \(\exp (-\Phi (\eta ))\)-expansion function method are utilized to handle this problem. These methods yield various innovative and fascinating solutions, including trigonometric, exponential, periodic, bright, singular, dark, and rational solutions, as well as their constraint conditions. Moreover the modulation instability (MI) of the consider model is also investigated. For each solution discovered, 2D, 3D, and contour plots are also sketched to clarify their physical configuration. The reported solutions enhance the previously established results. The solutions demonstrate that these methods are efficient and effective for locating traveling wave solutions and could be a beneficial tool for handling other complex nonlinear partial differential equations (NLPDEs) emerge in diversified scientific fields such as hydrodynamics, nonlinear optics, nonlinear fibers and plasmas.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors comment: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.]

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, 50700, Pakistan

    Jamshad Ahmad, Zulaikha Mustafa &  Shafqat-Ur-Rehman

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  1. Jamshad Ahmad
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  2. Zulaikha Mustafa
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  3. Shafqat-Ur-Rehman
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Contributions

JA: Resources, acquisition, Supervision, Writing - review and editing, Validation. ZM: Conceptualization, Methodology, Software, Writing - original draft. SUR: Software, Formal analysis, Writing-review and editing.

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Correspondence to Jamshad Ahmad.

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Ahmad, J., Mustafa, Z. & Shafqat-Ur-Rehman Dynamics of exact solutions of nonlinear resonant Schrödinger equation utilizing conformable derivatives and stability analysis. Eur. Phys. J. D 77, 123 (2023). https://doi.org/10.1140/epjd/s10053-023-00703-8

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