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Complex solutions to the higher-order nonlinear boussinesq type wave equation transform

Abstract

The higher-order nonlinear Boussinesq type wave equation describes the propagation of small amplitude long capillary–gravity waves on the surface of shallow water. Mathematical physics, shallow water waves, fluid dynamics, and fluid movement are all examples of this model. To acquire exact solutions in the form of solitary wave and complex functions solutions, we use the \(\left( {m + \frac{1}{{G^{\prime}}}} \right)\)-expansion method. These results aid mathematicians and physicians in comprehending the model's physical phenomena. This approach may be employed on different models in order to generate whole new solutions for nonlinear PDEs encountered in mathematical physics.

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Correspondence to S. Ş. Ş. Kiliç.

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Kiliç, S.Ş.Ş., Çelik, E. Complex solutions to the higher-order nonlinear boussinesq type wave equation transform. Ricerche mat (2022). https://doi.org/10.1007/s11587-022-00698-1

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  • DOI: https://doi.org/10.1007/s11587-022-00698-1

Keywords

  • The higher-order nonlinear Boussinesq type wave equation
  • \(\left( {m + \frac{1}{{G^{\prime}}}} \right)\)-expansion method
  • Complex soliton solutions
  • Physical phenomena

Mathematics Subject Classification

  • 65Lxx
  • 65Mxx
  • 65Zxx
  • 97Rxx
  • 97Mxx
  • 97Exx