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Innovative integration technologies for Kaup-Newell model: sub-picosecond optical pulses in birefringent fibers
  • Bahadır Kopçasız,
  • Fatma Nur Kaya Sağlam
Bahadır Kopçasız
Bursa Uludag Universitesi Fen Edebiyat Fakultesi

Corresponding Author:bkopcasz@gmail.com

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Fatma Nur Kaya Sağlam
Tekirdag Namik Kemal Universitesi Matematik Bolumu
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Abstract

This research deals with the Kaup-Newell model (KNM), a class of nonlinear Schrödinger equations with important applications in plasma physics and nonlinear optics. Soliton solutions are essential for analyzing nonlinear wave behaviors in different physical systems, and the KNM is also significant in this context. The model’s ability to represent sub-picosecond pulses makes it a significant tool for the research of nonlinear optics and plasma physics. Overall, the KNM is an important research domain in these areas, with ongoing efforts focused on understanding its various solutions and potential applications. A new version of the generalized exponential rational function method (nGERFM) and ( G ′ G 2 ) -expansion function methods are utilized to discover diverse soliton solutions. The nGERFM facilitates the generation of multiple solution types, including singular, shock, singular periodic, exponential, combo trigonometric, and hyperbolic solutions in mixed forms. Thanks to ( G ′ G 2 ) -expansion function method, we obtain trigonometric, hyperbolic, and rational solutions. The modulation instability (MI) of the proposed model is examined, with numerical simulations complementing the analytical results to provide a better understanding of the solutions’ dynamic behavior. These results offer a foundation for future research, making the solutions effective, manageable, and reliable for tackling complex nonlinear problems. The methodologies used in this study are robust, influential, and practicable for diverse nonlinear partial differential equations (NLPDEs); to our knowledge, for this equation, these methods of investigation have not been explored before. The accuracy of each solution has been verified using the Maple software program.
14 Jul 2024Submitted to Mathematical Methods in the Applied Sciences
15 Jul 2024Submission Checks Completed
15 Jul 2024Assigned to Editor
24 Jul 2024Review(s) Completed, Editorial Evaluation Pending
24 Jul 2024Reviewer(s) Assigned
02 Oct 2024Editorial Decision: Revise Major