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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, University of Kalyani, Kalyani, 741235, India

    Amiya Das & Niladri Ghosh

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  1. Amiya Das
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  2. Niladri Ghosh
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Correspondence to Amiya Das.

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Communicated by Pierangelo Marcati.

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Appendix

Appendix

Table 1 Relation between (A, B, C) and \(F(\xi )\) in (22)
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Das, A., Ghosh, N. Bifurcation of traveling waves and exact solutions of Kadomtsev–Petviashvili modified equal width equation with fractional temporal evolution. Comp. Appl. Math. 38, 9 (2019). https://doi.org/10.1007/s40314-019-0762-3

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