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Dynamics of Solitons in High-Order Nonlinear Schrödinger Equations in Fiber Optics

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Mathematics Applied to Engineering, Modelling, and Social Issues

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 200))

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Abstract

In optical fibers, the higher order nonlinear Schrödinger equation (NLSE) with cubic-quintic nonlinearity describes the propagation of extremely short pulses. We construct kink, bright and dark solitons of a generalized higher order NLSE in a cubic-quintic non-Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physical science and engineering. Moreover, we also present the formation conditions on solitary wave parameters in which kink, dark and bright solitons can exist for this media. We graphically illustrate the collision of the constructed soliton solutions that help realize the physical phenomena of NLSE. We also outline descriptions of various issues on integrability. We discuss the stability of the model in normal dispersion and anomalous regime by using the modulation instability analysis. Many other types of such models arising in applied sciences can also be solved by these reliable, powerful and effective methods.

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Authors and Affiliations

  1. Department of Mathematics, and Interdisciplinary Research Institute for the Sciences (IRIS), California State University - Northridge, Northridge, CA, 91330-8313, USA

    Gholam-Ali Zakeri

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  1. Gholam-Ali Zakeri
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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Frank T. Smith

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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Zakeri, GA. (2019). Dynamics of Solitons in High-Order Nonlinear Schrödinger Equations in Fiber Optics. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_7

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