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Computational soliton solutions to \((3+1)\)-dimensional generalised Kadomtsev–Petviashvili and \((2+1)\)-dimensional Gardner–Kadomtsev–Petviashvili models and their applications

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Abstract

In this paper, the auxiliary equation method is successfully applied to compute analytical solutions for \((3+1)\)-dimensional generalised Kadomtsev–Petviashvili and \((2+1)\)-dimensional Gardner–Kadomtsev–Petviashvili equations, by introducing simple transformations. These results hold numerous travelling wave solutions that are of key importance which provide a powerful mathematical tool for solving nonlinear wave equations in recent era of applied science and engineering. The method can also be extended to other nonlinear evolution models arising in contemporary physics.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan , 430074, People’s Republic of China

    Kalim U Tariq

  2. Department of Mathematics, Mirpur University of Science and Technology, Mirpur (AJK) , 10250, Pakistan

    Kalim U Tariq

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

    Aly R Seadawy & Sultan Z Alamri

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

    Aly R Seadawy

Authors
  1. Kalim U Tariq
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  2. Aly R Seadawy
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  3. Sultan Z Alamri
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Correspondence to Aly R Seadawy.

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Tariq, K.U., Seadawy, A.R. & Alamri, S.Z. Computational soliton solutions to \((3+1)\)-dimensional generalised Kadomtsev–Petviashvili and \((2+1)\)-dimensional Gardner–Kadomtsev–Petviashvili models and their applications. Pramana - J Phys 91, 68 (2018). https://doi.org/10.1007/s12043-018-1641-y

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  • DOI: https://doi.org/10.1007/s12043-018-1641-y

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