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

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

JOURNAL=Frontiers in Physics

VOLUME=7

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00197

DOI=10.3389/fphy.2019.00197

ISSN=2296-424X

ABSTRACT=<p>In this paper, we use the modified exponential function method in terms of <italic>K</italic><sup><italic>f</italic>(<italic>x</italic>)</sup> instead of <italic>e</italic><sup><italic>f</italic>(<italic>x</italic>)</sup>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.</p>