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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

  • Behzad Ghanbari
  • Chun-Ku KuoEmail author
Regular Article

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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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Engineering ScienceKermanshah University of TechnologyKermanshahIran
  2. 2.Department of Biomedical Engineering, Faculty of Engineering and Natural SciencesBahçeşehir UniversityIstanbulTurkey
  3. 3.Department of Aeronautics and AstronauticsAir Force AcademyKaohsiungTaiwan

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