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A novel technique to construct exact solutions for nonlinear partial differential equations

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Abstract.

The aim of the manuscript is to present a new exact solver of nonlinear partial differential equations. The proposed technique is developed by extending the \( \phi^{6}\)-model expansion method as a known method. The corresponding exact solutions are given in terms of Jacobi elliptic functions. Some new optical solutions of the resonant nonlinear Schrödinger equation are constructed within this newly proposed method. For some specific choices of the modulus of Jacobi elliptic functions, various solutions of the equation are introduced. Some numerical simulations are also included to emphasize that all parameters have major influences for the solitary waves behaviours. The proposed technique is very simple and straightforward, and can be employed to solve other non-linear partial differential equations.

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Authors and Affiliations

  1. Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran

    Behzad Ghanbari

  2. Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahcesehir University, 34349, Istanbul, Turkey

    Behzad Ghanbari

  3. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  4. Institute of Space Sciences, Magurele-Bucharest, P.O.Box, R 76900, MG-23, Romania

    Dumitru Baleanu

Authors
  1. Behzad Ghanbari
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  2. Dumitru Baleanu
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Correspondence to Dumitru Baleanu.

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Ghanbari, B., Baleanu, D. A novel technique to construct exact solutions for nonlinear partial differential equations. Eur. Phys. J. Plus 134, 506 (2019). https://doi.org/10.1140/epjp/i2019-13037-9

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