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Bifurcation and exact traveling wave solutions to a conformable nonlinear Schrödinger equation using a generalized double auxiliary equation method

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Abstract

This paper deals with a nonlinear Schrödinger equation in the sense of conformable derivative. Bifurcations and phase portraits are first proposed by using bifurcation theory, which investigates the dynamical behavior of this equation. This bifurcation theory classifies the plausible solutions to infinite periodic wave solutions, periodic wave solutions, two kink (anti-kink) wave solutions, and two families of breaking wave solutions. A generalized double auxiliary equation approach that generates three families of exact exact traveling wave solutions is then proposed using the conformable operator under various parameter conditions. The 3D behavior of various solutions with absolute real and imaginary parts is displayed. The obtained results show that the proposed methodology is efficient and applicable to a broad class of conformable nonlinear partial differential equations in mathematical physics.

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No funding was received to assist with the preparation of this manuscript.

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Authors and Affiliations

  1. Higher School of Management and Digital Economy, Tipaza, Kolea, Algeria

    Boubekeur Gasmi

  2. Department of Management Information System and Production Management, College of Business and Economics, Qassim University, P.O. BOX 6666, 51452, Buraidah, Saudi Arabia

    Alaaeddin Moussa, Yazid Mati & Lama Alhakim

  3. Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, Turkey

    Haci Mehmet Baskonus

Authors
  1. Boubekeur Gasmi
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  2. Alaaeddin Moussa
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  3. Yazid Mati
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  4. Lama Alhakim
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  5. Haci Mehmet Baskonus
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Contributions

BG:Supervision. AAM:Methodology. YM: Writing and editing. LAA:Validation. HMB:Supervisor, Editing, Writing original draft.

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Correspondence to Haci Mehmet Baskonus.

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Gasmi, B., Moussa, A., Mati, Y. et al. Bifurcation and exact traveling wave solutions to a conformable nonlinear Schrödinger equation using a generalized double auxiliary equation method. Opt Quant Electron 56, 18 (2024). https://doi.org/10.1007/s11082-023-05578-y

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