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Soliton solutions to the non-local Boussinesq equation by multiple exp-function scheme and extended Kudryashov’s approach

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Abstract

In this paper, we study the exact solutions of non-local Boussinesq equation (nlBq) which appears in many scientific fields. We generate dark solitons, singular solitons, a new family of solitons and combo dark–singular soliton-type solutions of nlBq by the extended Kudryashov’s algorithm. Additional solutions such as singular periodic solutions also fall out of this integration scheme. Also, one-soliton, two-soliton and three-soliton type solutions are presented using multiple exp-function algorithm. Lastly, Lie symmetry analysis with the new similarity reductions is also examined.

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Authors and Affiliations

  1. Material Science Innovation and Modelling Focus Area, School of Mathematical and Statistical Sciences, North-West University, Private Bag X 2046, Mmabatho, 2735, South Africa

    Abdullahi Rashid Adem

  2. Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 , Bursa, Turkey

    Yakup Yildirim & Emrullah Yaşar

Authors
  1. Abdullahi Rashid Adem
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  2. Yakup Yildirim
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  3. Emrullah Yaşar
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Correspondence to Emrullah Yaşar.

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Adem, A.R., Yildirim, Y. & Yaşar, E. Soliton solutions to the non-local Boussinesq equation by multiple exp-function scheme and extended Kudryashov’s approach. Pramana - J Phys 92, 24 (2019). https://doi.org/10.1007/s12043-018-1679-x

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  • DOI: https://doi.org/10.1007/s12043-018-1679-x

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