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New exact wave solutions of the variable-coefficient (1 + 1)-dimensional Benjamin-Bona-Mahony and (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations via the generalized exponential rational function method

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Abstract.

In this paper, the variable-coefficient (1 + 1)-dimensional Benjamin-Bona-Mahony (BBM) and (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equations are investigated via the generalized exponential rational function method (GERFM). This paper proceeds step-by-step with increasing detail about derivation processes, first illustrating the algorithms of the proposed method and then exploiting an even deeper connection between the derived solutions with the GERFM. As a result, versions of variable-coefficient exact solutions are formally generated. The presented solutions exhibit abundant physical phenomena. Particularly, upon choosing appropriate parameters, we demonstrate a variety of traveling waves in figures. Finally, the results indicate that free parameters can drastically influence the existence of solitary waves, their nature, profile, and stability. They are applicable to enrich the dynamical behavior of the (1 + 1) and (2 + 1)-dimensional nonlinear wave in fluids, plasma and others.

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Author information

Authors and Affiliations

  1. Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran

    Behzad Ghanbari

  2. Department of Biomedical Engineering, Faculty of Engineering and Natural Sciences, Bahçeşehir University, 34349, Istanbul, Turkey

    Behzad Ghanbari

  3. Department of Aeronautics and Astronautics, Air Force Academy, 820, Kaohsiung, Taiwan

    Chun-Ku Kuo

Authors
  1. Behzad Ghanbari
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  2. Chun-Ku Kuo
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Correspondence to Chun-Ku Kuo.

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Ghanbari, B., Kuo, CK. New exact wave solutions of the variable-coefficient (1 + 1)-dimensional Benjamin-Bona-Mahony and (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations via the generalized exponential rational function method. Eur. Phys. J. Plus 134, 334 (2019). https://doi.org/10.1140/epjp/i2019-12632-0

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  • DOI: https://doi.org/10.1140/epjp/i2019-12632-0

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