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Original Research ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Phys. | doi: 10.3389/fphy.2019.00197

Complex and real optical soliton properties of the paraxial nonlinear Schrödinger equation in Kerr media with M-fractional

  • 1Yunnan Normal University, China
  • 2University of Zakho, Iraq
  • 3University of Duhok, Iraq
  • 4Harran University, Turkey
  • 5Firat University, Turkey

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 nonlinear 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 solution, singular soliton solutions, kink-type soliton solution and periodic dark-singular soliton solutions for M-fractional paraxial nonlinear 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: paraxial wave equation, Complex soliton, MEFM, extended sinh-Gordon method, M-fractional

Received: 21 Sep 2019; Accepted: 06 Nov 2019.

Copyright: © 2019 Gao, Ismael, Mohammed, Baskonus and Bulut. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Mx. Wei Gao, Yunnan Normal University, Kunming, China, gaowei@ynnu.edu.cn