American Journal of Optics and Photonics

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Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions

Received: 19 August 2018    Accepted: 06 September 2018    Published: 14 December 2018
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Abstract

In this paper, we modify with an appropriate analytical technique, the characteristics of the optical fiber through the modification of the coefficients of the highly nonlinear partial differential equation, which initially governs the dynamics of the propagation in such a wave guide. The procedure consists to assign arbitrary coefficients to the various terms of the established nonlinear partial differential equation, such as the one that embodies the propagation dynamics in a strongly nonlinear optical fiber and subsequently establishing the constraint equations linking these coefficients and thus the analys is makes it possible to enumerate the criteria for which obtaining the desired solutions is possible. These coefficients are like indicators which characterize the various modifications made in this medium of transmission. The nonlinear evolution equation that served as mathematical model for this study is the higher-order nonlinear Schrödinger equation which better describes the propagation of an ultrafast pulse in an optical fiber. The use of the Bogning-Djeumen Tchaho-Kofané method enabled not only to establish the constraint relations, but also the solitary wave solutions and plane wave solutions. We want through the results obtained in this article to give the specialists of the manufacture of transmission media such as optical fiber, to consider the modification of the properties of this wave guide during manufacture, depending on the type of signal that one wants to propagate in this case notably the solitary wave.

DOI 10.11648/j.ajop.20180603.12
Published in American Journal of Optics and Photonics (Volume 6, Issue 3, September 2018)
Page(s) 31-41
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Schrödinger Equation, Higher-Order Nonlinear Effects, Solitary Wave Solution, Periodic Travelling Wave Solutions, Bogning–Djeumen–Kofané Method

References
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Author Information
  • Department of Physics, Faculty of Science, University of Yaounde I, Yaoundé, Cameroon; African Center of Excellence in Information Technology and Telecommunications, University of Yaoundé I, Yaoundé, Cameroon

  • Department of Physics, Higher Teacher Training College, University of Bamenda, Bamenda, Cameroon

  • Department of Physics, Faculty of Science, University of Yaounde I, Yaoundé, Cameroon; African Center of Excellence in Information Technology and Telecommunications, University of Yaoundé I, Yaoundé, Cameroon

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  • APA Style

    Rodrique Njikue, Jean Roger Bogning, Timoleon Crépin Kofané. (2018). Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions. American Journal of Optics and Photonics, 6(3), 31-41. https://doi.org/10.11648/j.ajop.20180603.12

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    ACS Style

    Rodrique Njikue; Jean Roger Bogning; Timoleon Crépin Kofané. Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions. Am. J. Opt. Photonics 2018, 6(3), 31-41. doi: 10.11648/j.ajop.20180603.12

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    AMA Style

    Rodrique Njikue, Jean Roger Bogning, Timoleon Crépin Kofané. Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions. Am J Opt Photonics. 2018;6(3):31-41. doi: 10.11648/j.ajop.20180603.12

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  • @article{10.11648/j.ajop.20180603.12,
      author = {Rodrique Njikue and Jean Roger Bogning and Timoleon Crépin Kofané},
      title = {Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions},
      journal = {American Journal of Optics and Photonics},
      volume = {6},
      number = {3},
      pages = {31-41},
      doi = {10.11648/j.ajop.20180603.12},
      url = {https://doi.org/10.11648/j.ajop.20180603.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajop.20180603.12},
      abstract = {In this paper, we modify with an appropriate analytical technique, the characteristics of the optical fiber through the modification of the coefficients of the highly nonlinear partial differential equation, which initially governs the dynamics of the propagation in such a wave guide. The procedure consists to assign arbitrary coefficients to the various terms of the established nonlinear partial differential equation, such as the one that embodies the propagation dynamics in a strongly nonlinear optical fiber and subsequently establishing the constraint equations linking these coefficients and thus the analys is makes it possible to enumerate the criteria for which obtaining the desired solutions is possible. These coefficients are like indicators which characterize the various modifications made in this medium of transmission. The nonlinear evolution equation that served as mathematical model for this study is the higher-order nonlinear Schrödinger equation which better describes the propagation of an ultrafast pulse in an optical fiber. The use of the Bogning-Djeumen Tchaho-Kofané method enabled not only to establish the constraint relations, but also the solitary wave solutions and plane wave solutions. We want through the results obtained in this article to give the specialists of the manufacture of transmission media such as optical fiber, to consider the modification of the properties of this wave guide during manufacture, depending on the type of signal that one wants to propagate in this case notably the solitary wave.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions
    AU  - Rodrique Njikue
    AU  - Jean Roger Bogning
    AU  - Timoleon Crépin Kofané
    Y1  - 2018/12/14
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ajop.20180603.12
    DO  - 10.11648/j.ajop.20180603.12
    T2  - American Journal of Optics and Photonics
    JF  - American Journal of Optics and Photonics
    JO  - American Journal of Optics and Photonics
    SP  - 31
    EP  - 41
    PB  - Science Publishing Group
    SN  - 2330-8494
    UR  - https://doi.org/10.11648/j.ajop.20180603.12
    AB  - In this paper, we modify with an appropriate analytical technique, the characteristics of the optical fiber through the modification of the coefficients of the highly nonlinear partial differential equation, which initially governs the dynamics of the propagation in such a wave guide. The procedure consists to assign arbitrary coefficients to the various terms of the established nonlinear partial differential equation, such as the one that embodies the propagation dynamics in a strongly nonlinear optical fiber and subsequently establishing the constraint equations linking these coefficients and thus the analys is makes it possible to enumerate the criteria for which obtaining the desired solutions is possible. These coefficients are like indicators which characterize the various modifications made in this medium of transmission. The nonlinear evolution equation that served as mathematical model for this study is the higher-order nonlinear Schrödinger equation which better describes the propagation of an ultrafast pulse in an optical fiber. The use of the Bogning-Djeumen Tchaho-Kofané method enabled not only to establish the constraint relations, but also the solitary wave solutions and plane wave solutions. We want through the results obtained in this article to give the specialists of the manufacture of transmission media such as optical fiber, to consider the modification of the properties of this wave guide during manufacture, depending on the type of signal that one wants to propagate in this case notably the solitary wave.
    VL  - 6
    IS  - 3
    ER  - 

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