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Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

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Abstract.

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

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Author information

Authors and Affiliations

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

    Aly R. Seadawy

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

    Aly R. Seadawy

  3. Graduate School of Systems and Information Engineering, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, Japan

    Dipankar Kumar

  4. Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, 8100, Gopalganj, Bangladesh

    Dipankar Kumar

  5. Department of General Educational Development, Daffodil International University, Dhaka, Bangladesh

    Anuz Kumar Chakrabarty

Authors
  1. Aly R. Seadawy
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  2. Dipankar Kumar
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  3. Anuz Kumar Chakrabarty
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Correspondence to Aly R. Seadawy.

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Seadawy, A.R., Kumar, D. & Chakrabarty, A.K. Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method. Eur. Phys. J. Plus 133, 182 (2018). https://doi.org/10.1140/epjp/i2018-12027-9

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  • DOI: https://doi.org/10.1140/epjp/i2018-12027-9

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