Analytical treatments of the space–time fractional coupled nonlinear Schrödinger equations

  • Mehrdad Lakestani
  • Jalil ManafianEmail author


Under investigation in this work is a (\(2+1\))-dimensional the space–time fractional coupled nonlinear Schrödinger equations, which describes the amplitudes of circularly-polarized waves in a nonlinear optical fiber. With the aid of conformable fractional derivative and the fractional wave transformation, we derive the analytical soliton solutions in the form of rational soliton, periodic soliton, hyperbolic soliton solutions by four integration method, namely, the extended trial equation method, the \(\exp (-\,\Omega (\eta ))\)-expansion method and the improved \(\tan (\phi (\eta )/2)\)-expansion method and semi-inverse variational principle method. Based on the the extended trial equation method, we derive the several types of solutions including singular, kink-singular, bright, solitary wave, compacton and elliptic function solutions. Under certain condition, the 1-soliton, bright, singular solutions are driven by semi-inverse variational principle method. Based on the analytical methods, we find that the solutions give birth to the dark solitons, the bright solitons, combine dark-singular, kink, kink-singular solutions with fractional order for nonlinear fractional partial differential equations arise in nonlinear optics.


Conformable time-fractional equations The space–time fractional coupled nonlinear Schrödinger equations The extended trial equation method The \(\exp (-~\Omega (\eta ))\)-expansion method The \(\tan (\phi (\eta )/2)\)-expansion method The semi-inverse variational principle method 



This paper is published as part of a research project supported by the University of Tabriz Research Affairs Office.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematical SciencesUniversity of TabrizTabrizIran

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