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On soliton solutions of time fractional form of Sawada–Kotera equation

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Abstract

Soliton solutions are of utmost importance among traveling wave solutions since they act as a bridge between mathematics and physics. This paper investigates time fractional form of fifth-order Sawada–Kotera equation resulting in different forms of exact and approximate soliton solutions including singular, periodic and dark soliton solutions. The time fractional derivative is used in the Caputo sense throughout the study. The effectiveness of trial equation method is seen in determining exact solutions, whereas residual power series method is employed for its high precision and reliability in calculating approximate solutions of the model. Multiple soliton solutions are also determined by the aid of Hirota’s method. The results are compared with a numerical method, and the graphical representation of all the obtained solutions is shown for different values of the fractional parameter. The time evolution of all solutions is also represented in 2D plots. These findings are highly encouraging to explore other nonlinear fractional models.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, China

    Usman Afzal

  2. Department of Mathematics, University of the Punjab, Lahore, Pakistan

    Nauman Raza & Isma Ghulam Murtaza

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  1. Usman Afzal
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  2. Nauman Raza
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  3. Isma Ghulam Murtaza
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Correspondence to Usman Afzal.

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Afzal, U., Raza, N. & Murtaza, I.G. On soliton solutions of time fractional form of Sawada–Kotera equation. Nonlinear Dyn 95, 391–405 (2019). https://doi.org/10.1007/s11071-018-4571-9

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  • DOI: https://doi.org/10.1007/s11071-018-4571-9

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