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Extended generalized \((Zakh\frac{G^{\prime }}{G})\)-expansion method for solving the nonlinear quantum Zakharov–Kuznetsov equation

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Abstract

In this article, we apply the extended generalized \((\frac{G^{\prime }}{G})\)-expansion method combined with the Jacobi elliptic equation to find new exact solutions of the nonlinear quantum Zakharov–Kuznetsov (QZK) equation with the aid of computer algebraic system Maple. Soliton solutions, periodic solutions, rational functions solutions and Jacobi elliptic functions solutions are obtained. Based on reductive perturbation technique and a series of transformation, the nonlinear QZK had been derived by many authors which can be reduced to a nonlinear ordinary differential equation (ODE) using the wave transformation. The extended generalized \((\frac{G^{\prime }}{G})\)-expansion method is straightforward and concise, and it can also be applied to other nonlinear PDEs in mathematical physics.

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Acknowledgments

The authors wish to thank the referee for his comments on this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    E. M. E. Zayed

  2. Department of Mathematics, Faculty of Science, Elmergib University, Msallata, Libya

    K. A. E. Alurrfi

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  1. E. M. E. Zayed
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  2. K. A. E. Alurrfi
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Correspondence to E. M. E. Zayed.

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Zayed, E.M.E., Alurrfi, K.A.E. Extended generalized \((Zakh\frac{G^{\prime }}{G})\)-expansion method for solving the nonlinear quantum Zakharov–Kuznetsov equation. Ricerche mat. 65, 235–254 (2016). https://doi.org/10.1007/s11587-016-0276-x

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  • DOI: https://doi.org/10.1007/s11587-016-0276-x

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