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Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models

Received: 4 October 2018     Accepted: 7 November 2018     Published: 18 December 2018
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Abstract

The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.

Published in American Journal of Applied Mathematics (Volume 6, Issue 5)
DOI 10.11648/j.ajam.20180605.11
Page(s) 149-158
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), 2018. Published by Science Publishing Group

Keywords

Coupled Classical Boussinesq Equation, Boussinesq-Kadomtsev-Petviashili Equation, Solitary Wave Solution, Periodic Wave Solution

References
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Cite This Article
  • APA Style

    M. Mashiur Rahhman, Ayrin Aktar, Kamalesh Chandra Roy. (2018). Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. American Journal of Applied Mathematics, 6(5), 149-158. https://doi.org/10.11648/j.ajam.20180605.11

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    ACS Style

    M. Mashiur Rahhman; Ayrin Aktar; Kamalesh Chandra Roy. Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. Am. J. Appl. Math. 2018, 6(5), 149-158. doi: 10.11648/j.ajam.20180605.11

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    AMA Style

    M. Mashiur Rahhman, Ayrin Aktar, Kamalesh Chandra Roy. Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. Am J Appl Math. 2018;6(5):149-158. doi: 10.11648/j.ajam.20180605.11

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  • @article{10.11648/j.ajam.20180605.11,
      author = {M. Mashiur Rahhman and Ayrin Aktar and Kamalesh Chandra Roy},
      title = {Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models},
      journal = {American Journal of Applied Mathematics},
      volume = {6},
      number = {5},
      pages = {149-158},
      doi = {10.11648/j.ajam.20180605.11},
      url = {https://doi.org/10.11648/j.ajam.20180605.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180605.11},
      abstract = {The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.},
     year = {2018}
    }
    

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    T1  - Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models
    AU  - M. Mashiur Rahhman
    AU  - Ayrin Aktar
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    N1  - https://doi.org/10.11648/j.ajam.20180605.11
    DO  - 10.11648/j.ajam.20180605.11
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20180605.11
    AB  - The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.
    VL  - 6
    IS  - 5
    ER  - 

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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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