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More general families of exact solitary wave solutions of the nonlinear Schrödinger equation with their applications in nonlinear optics

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Abstract.

In this article we analytically studied the complex nonlinear Schrödinger equation with Kerr law nonlinearity using the auxiliary equation mapping method, as a result, we found a series of more general and new families of exact solutions, which are more powerful in the development of soliton dynamics, quantum plasma, adiabatic parameter dynamics, biomedical problems, fluid dynamics, industrial studies, nonlinear optics and many other fields. The calculations demonstrate that this method is more reliable, straightforward and effective to analytically study other nonlinear complicated physical problems modeled by complex nonlinear partial differential equations arising in mathematical physics, hydrodynamics, fluid mechanics, mathematical biology, plasma physics, engineering disciplines, chemistry and many other natural sciences. We have also expressed our solutions graphically with the help of Mathematica 10.4 to physically understand the behavior of different shapes of solutions including kink-type, anti-kink-type, half-bright and dark solitons.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, 150001, Harbin, China

    Nadia Cheemaa & Sheng Chen

  2. Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Aly R. Seadawy

  3. Mathematics Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt

    Aly R. Seadawy

Authors
  1. Nadia Cheemaa
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  2. Aly R. Seadawy
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  3. Sheng Chen
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Corresponding author

Correspondence to Aly R. Seadawy.

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Cheemaa, N., Seadawy, A.R. & Chen, S. More general families of exact solitary wave solutions of the nonlinear Schrödinger equation with their applications in nonlinear optics. Eur. Phys. J. Plus 133, 547 (2018). https://doi.org/10.1140/epjp/i2018-12354-9

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  • DOI: https://doi.org/10.1140/epjp/i2018-12354-9

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