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Exact periodic and explicit solutions of the conformable time fractional Ginzburg Landau equation

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Abstract

The Ginzburg–Landau (GL) equation is one of the most important nonlinear equation in physics. It is used to model a vast variety of phenomena in physics like nonlinear waves, second order phase transitions, Bose–Einstein condensation, superfluidity, superconductivity, liquid crystals and strings in field theory. In this work, new exact, periodic and explicit solutions of a time fractional GL equation involving conformable fractional derivatives with Kerr law nonlinearity have been found. The Kerr law nonlinearity is due to the non-harmonic motion of electrons under the influence of an applied field. To determine the solution of the model, we have employed a couple of integration algorithms, solitary wave ansatz and \(\exp (-\varphi ({\chi }\))) methods. New periodic and hyperbolic soliton solutions are found as well as the constraint condition for the existence of the solution.

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Acknowledgements

We would like to thank reviewers for their observations, careful assessment, valuable suggestions and fruitful remarks which have improved the quality of initial version of the research paper.

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  1. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan

    Nauman Raza

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  1. Nauman Raza
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Correspondence to Nauman Raza.

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Raza, N. Exact periodic and explicit solutions of the conformable time fractional Ginzburg Landau equation. Opt Quant Electron 50, 154 (2018). https://doi.org/10.1007/s11082-018-1420-5

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