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New \(\phi^{6}\)-model expansion method and its applications to the resonant nonlinear Schrödinger equation with parabolic law nonlinearity

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Abstract.

With the aid of symbolic computation, the new \(\phi^{6}\)-model expansion method is applied, in this article, for the first time to the resonant nonlinear Schrödinger equation with parabolic law nonlinearity to find families of Jacobi elliptic function solutions. In particular, when the modulus of the Jacobi elliptic functions tends to one or to zero, we can get the hyperbolic and trigonometric function solutions, respectively. This new method presents a wider applicability for handling the nonlinear partial differential equations. Comparison of our new results with the well-known results are given. At the end of this paper, we use the solutions of the Liénard equation to find more different solutions for the proposed resonant nonlinear Schrödinger equation mentioned above.

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Authors and Affiliations

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

    Elsayed M. E. Zayed & Mona E. M. Elshater

  2. Mathematics Department, Faculty of Education and Science, Taiz University, Taiz, Yemen

    Abdul-Ghani Al-Nowehy

Authors
  1. Elsayed M. E. Zayed
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  2. Abdul-Ghani Al-Nowehy
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  3. Mona E. M. Elshater
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Correspondence to Abdul-Ghani Al-Nowehy.

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Zayed, E.M.E., Al-Nowehy, AG. & Elshater, M.E.M. New \(\phi^{6}\)-model expansion method and its applications to the resonant nonlinear Schrödinger equation with parabolic law nonlinearity. Eur. Phys. J. Plus 133, 417 (2018). https://doi.org/10.1140/epjp/i2018-12288-2

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