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Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method

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Abstract

This paper secures new nematicons in liquid crystals from its governing equation by extended sinh-Gordon equation expansion method with the aid of symbolic computational package Maple. The two laws of nonlinearity, namely Kerr and parabolic laws are studied. As outcomes, some new explicit complex hyperbolic and complex trigonometric function solutions are derived regarding dark, bright, combined dark–bright, singular, combined singular optical, periodic wave, dipole soliton solutions and others. To show the real physical meaning of the derived results, three dimensional graphs with contours and two dimensional graphs are prepared under the choice of proper values of the arbitrary parameters. The derived solutions have been checked back into their corresponding equations with the symbolic computational package Maple. All the combined solutions are found to be new, which may play an important role in the context of liquid crystals. The applied method is found to provide a powerful tool for extracting exact solitary wave solutions and overcome the difficulties of the solitary wave ansatz method.

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Acknowledgments

We would like to thank both the referees for very useful comments and suggestions that improved this manuscript.

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Authors and Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan

    Dipankar Kumar

  2. Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, Bangladesh

    Dipankar Kumar

  3. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, University of Chinese Academy of Sciences, Beijing, China

    Atish Kumar Joardar

  4. Department of Mathematics, Islamic University, Kushtia, 7003, Bangladesh

    Atish Kumar Joardar

  5. Department of Mathematics, University of Rajshahi, Rajshahi, 6205, Bangladesh

    Ashabul Hoque & Gour Chandra Paul

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  1. Dipankar Kumar
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Correspondence to Gour Chandra Paul.

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Kumar, D., Joardar, A.K., Hoque, A. et al. Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method. Opt Quant Electron 51, 212 (2019). https://doi.org/10.1007/s11082-019-1917-6

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