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An investigation of fractional complex Ginzburg–Landau equation with Kerr law nonlinearity in the sense of conformable, beta and M-truncated derivatives

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Abstract

Complex Ginzburg–Landau equation is widely used for investigating superconductivity, strings in field theory, non-linear dynamics of fibre lasers and ultra fast optics. In this paper, dark, bright, complexiton, singular and periodic optical solitons of fractional order complex Ginzburg–Landau equation have been retrieved with Kerr law nonlinearity. Abundant traveling wave solutions consisting of hyperbolic, trigonometric, exponential and rational function solutions are constructed. Exact solutions of the considered model have been extracted by using improved \(\tan \left( \frac{\psi (\zeta )}{2}\right)\)-expansion technique. A comparative study among the solutions has been exercised by implementing conformable, beta and M-truncated derivatives. Furthermore, graphical illustration of the comparison of the results obtained by the three derivatives has been reported as well.

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The computations involved in the work are done with the help of Maple and Mathematica.

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  1. Department of Mathematics, University of the Punjab, Lahore, 54590, Pakistan

    Maasoomah Sadaf, Ghazala Akram & Mirfa Dawood

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  1. Maasoomah Sadaf
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  2. Ghazala Akram
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Sadaf, M., Akram, G. & Dawood, M. An investigation of fractional complex Ginzburg–Landau equation with Kerr law nonlinearity in the sense of conformable, beta and M-truncated derivatives. Opt Quant Electron 54, 248 (2022). https://doi.org/10.1007/s11082-022-03570-6

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