Frontiers in Physics (Nov 2019)

Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional

  • Wei Gao,
  • Hajar F. Ismael,
  • Hajar F. Ismael,
  • Sizar A. Mohammed,
  • Haci Mehmet Baskonus,
  • Hasan Bulut

DOI
https://doi.org/10.3389/fphy.2019.00197
Journal volume & issue
Vol. 7

Abstract

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In this paper, we use the modified exponential function method in terms of Kf(x) instead of ef(x)and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrödinger equation. The novel complex and real optical soliton solutions are plotted in 2-D, 3-D with a contour plot. Moreover, the dark exact solutions, singular soliton solutions, kink-type soliton solution, and periodic dark-singular soliton solutions for M-fractional paraxial non-linear Schrödinger equation are constructed. We guarantee that all solutions are new and verified the main equation of the M-fractional paraxial wave equation. For existence, the constraint condition is also added.

Keywords