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Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics

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Abstract.

This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi’s elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Mohammad Mirzazadeh

  2. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100, Yozgat, Turkey

    Mehmet Ekici & Abdullah Sonmezoglu

  3. Department of Physics, Faculty of Science, Erciyes University, 38039, Kayseri, Turkey

    Sami Ortakaya

  4. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    Mostafa Eslami

  5. Department of Mathematical Sciences, Delaware State University, 19901-2277, Dover, DE, USA

    Anjan Biswas

  6. Department of Mathematics, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    Anjan Biswas

Authors
  1. Mohammad Mirzazadeh
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  2. Mehmet Ekici
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  3. Abdullah Sonmezoglu
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  4. Sami Ortakaya
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  5. Mostafa Eslami
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  6. Anjan Biswas
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Correspondence to Mehmet Ekici.

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Mirzazadeh, M., Ekici, M., Sonmezoglu, A. et al. Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics. Eur. Phys. J. Plus 131, 166 (2016). https://doi.org/10.1140/epjp/i2016-16166-7

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  • DOI: https://doi.org/10.1140/epjp/i2016-16166-7

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