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Bifurcation and new traveling wave solutions for (2 + 1)-dimensional nonlinear Nizhnik–Novikov–Veselov dynamical equation

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Abstract

The bifurcation theory for planar dynamical systems is applied to the traveling wave system corresponding to the \((2+1)\)-dimensional nonlinear Nizhnik–Novikov–Veselov dynamical equation. For certain values of the bifurcation parameters, we introduce new traveling wave solutions. These solutions are expressed in terms of elliptic Jacobi functions and Weierstrass elliptic function. These solutions are graphically clarified.

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Acknowledgements

The authors acknowledge the Deanship of Scientific Research at King Faisal University for the financial support under Nasher Track (Grant No. 186224)

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Authors and Affiliations

  1. Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsa, 31982, Saudi Arabia

    M. E. Elbrolosy & A. A. Elmandouh

  2. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

    M. E. Elbrolosy

  3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    A. A. Elmandouh

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  1. M. E. Elbrolosy
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  2. A. A. Elmandouh
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Correspondence to A. A. Elmandouh.

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Elbrolosy, M.E., Elmandouh, A.A. Bifurcation and new traveling wave solutions for (2 + 1)-dimensional nonlinear Nizhnik–Novikov–Veselov dynamical equation. Eur. Phys. J. Plus 135, 533 (2020). https://doi.org/10.1140/epjp/s13360-020-00546-x

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