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Modified Kudryashov method and its application to the fractional version of the variety of Boussinesq-like equations in shallow water

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Abstract

The present study emphasis to look for new closed form exact solitary wave solutions for the variety of fractional Boussinesq-like equations using the modified Kudryashov method with the help of symbolic computation. As a consequence, the modified Kudryashov method is successfully employed and acquired some new exact solitary wave solutions in terms of exponential based functions with fractional version. All solutions have been verified back into its corresponding equation with the aid of Maple package program. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in the field of oceanography.

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Authors and Affiliations

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

    D. Kumar

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

    D. Kumar

  3. Department of Mathematics, Razi University, Kermanshah, 67149, Iran

    M. T. Darvishi

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

    A. K. Joardar

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  1. D. Kumar
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  2. M. T. Darvishi
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  3. A. K. Joardar
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Correspondence to M. T. Darvishi.

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Kumar, D., Darvishi, M.T. & Joardar, A.K. Modified Kudryashov method and its application to the fractional version of the variety of Boussinesq-like equations in shallow water. Opt Quant Electron 50, 128 (2018). https://doi.org/10.1007/s11082-018-1399-y

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