American Journal of Applied Mathematics

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Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method

Received: 21 April 2019    Accepted: 13 June 2019    Published: 27 June 2019
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Abstract

This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.

DOI 10.11648/j.ajam.20190702.12
Published in American Journal of Applied Mathematics (Volume 7, Issue 2, April 2019)
Page(s) 49-57
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Novel Exponential Expansion Method, Boussinesq Equation, Solitary Wave Solutions, Periodic Solutions

References
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Author Information
  • Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh

  • Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh

  • Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh

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  • APA Style

    Ayrin Aktar, Md Mashiur Rahhman, Kamalesh Chandra Roy. (2019). Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. American Journal of Applied Mathematics, 7(2), 49-57. https://doi.org/10.11648/j.ajam.20190702.12

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    ACS Style

    Ayrin Aktar; Md Mashiur Rahhman; Kamalesh Chandra Roy. Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. Am. J. Appl. Math. 2019, 7(2), 49-57. doi: 10.11648/j.ajam.20190702.12

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    AMA Style

    Ayrin Aktar, Md Mashiur Rahhman, Kamalesh Chandra Roy. Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. Am J Appl Math. 2019;7(2):49-57. doi: 10.11648/j.ajam.20190702.12

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  • @article{10.11648/j.ajam.20190702.12,
      author = {Ayrin Aktar and Md Mashiur Rahhman and Kamalesh Chandra Roy},
      title = {Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method},
      journal = {American Journal of Applied Mathematics},
      volume = {7},
      number = {2},
      pages = {49-57},
      doi = {10.11648/j.ajam.20190702.12},
      url = {https://doi.org/10.11648/j.ajam.20190702.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20190702.12},
      abstract = {This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method
    AU  - Ayrin Aktar
    AU  - Md Mashiur Rahhman
    AU  - Kamalesh Chandra Roy
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    DO  - 10.11648/j.ajam.20190702.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    EP  - 57
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20190702.12
    AB  - This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.
    VL  - 7
    IS  - 2
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