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

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    Mehrdad Lakestani & Jalil Manafian

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  1. Mehrdad Lakestani
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  2. Jalil Manafian
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Correspondence to Jalil Manafian.

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Lakestani, M., Manafian, J. Analytical treatments of the space–time fractional coupled nonlinear Schrödinger equations. Opt Quant Electron 50, 396 (2018). https://doi.org/10.1007/s11082-018-1615-9

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