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Bifurcation of traveling waves and exact solutions of Kadomtsev–Petviashvili modified equal width equation with fractional temporal evolution

  • Amiya DasEmail author
  • Niladri Ghosh
Article
  • 37 Downloads

Abstract

The article is devoted in the study of the Kadomtsev–Petviashvili modified equal width equation with fractional temporal evolution in which modified Riemann–Liouville derivative is considered. We discuss the dynamical behavior of the system using bifurcation theory in different parametric regions. We also depict the phase portraits of the traveling wave solutions and obtain explicit traveling waves including solitary wave and breaking wave solution. We apply the \((G'/G)\)-expansion method and the F-expansion method along with fractional complex transformation, and obtain a large variety of exact traveling wave solutions which includes solitary wave, kink-type wave, and periodic wave solutions of the equation. Finally, we demonstrate remarkable features of the traveling wave solutions via interesting figures and phase portraits.

Keywords

Fractional differential equation KP equation Modified equal width equation Bifurcation theory Phase portraits \((G'/G)-\)Expansion method \(F-\)Expansion method Traveling wave solution Jacobi elliptic functions 

Mathematics Subject Classification

34K18 35C07 

Notes

Acknowledgements

This work is supported by Science and Engineering Research Board, Department of Science and Technology, Govt. of India (EEQ/2017/000150).

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KalyaniKalyaniIndia

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