Jacobi elliptic solutions, solitons and other solutions for the nonlinear Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity

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Abstract.

Based on several integration tools, namely the Riccati equation method, the Bernoulli equation method, the extended auxiliary equation method, the new mapping method and the \(\phi^{6}\)-model expansion method, we obtain many exact solutions including the optical bright-dark-singular soliton solutions, Jacobi elliptic solutions and trigonometric function solutions of the nonlinear Schrödinger equation (NLSE) with fourth-order dispersion and cubic-quintic nonlinearity, self-steeping and self-frequency shift effects which describes the propagation of an optical pulse in optical fibers. We compare the results yielding from these integration tools together with each others. Also, a comparison between our results in this paper and the well-known results are given.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesZagazig UniversityZagazigEgypt
  2. 2.Department of Mathematics, Faculty of Education and ScienceTaiz UniversityTaizYemen

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