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New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model

Received: 30 January 2018     Accepted: 11 February 2018     Published: 7 March 2018
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Abstract

One-dimensional parabolic-parabolic Keller-Segel (PP-KS) model of chemotaxis is considered. By using the generalized tanh function method, G'(/G)-expansion method and variable-separating method, plenty of new explicit exact solutions, including travelling wave solutions and non-travelling wave solutions, are obtained for the PP-KS model. Compared to the existing results, more new exact solutions are derived and the obtained solutions all have explicit expressions.

Published in Applied and Computational Mathematics (Volume 7, Issue 2)
DOI 10.11648/j.acm.20180702.13
Page(s) 50-57
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), 2018. Published by Science Publishing Group

Keywords

Keller-Segel Model, Generalized Tanh Function Method, (G'/G)-Expansion Method, Variable-Separating Method, Exact Solutions

References
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  • APA Style

    Lihua Zhang, Lixin Ma, Fengsheng Xu. (2018). New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model. Applied and Computational Mathematics, 7(2), 50-57. https://doi.org/10.11648/j.acm.20180702.13

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    ACS Style

    Lihua Zhang; Lixin Ma; Fengsheng Xu. New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model. Appl. Comput. Math. 2018, 7(2), 50-57. doi: 10.11648/j.acm.20180702.13

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    AMA Style

    Lihua Zhang, Lixin Ma, Fengsheng Xu. New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model. Appl Comput Math. 2018;7(2):50-57. doi: 10.11648/j.acm.20180702.13

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  • @article{10.11648/j.acm.20180702.13,
      author = {Lihua Zhang and Lixin Ma and Fengsheng Xu},
      title = {New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model},
      journal = {Applied and Computational Mathematics},
      volume = {7},
      number = {2},
      pages = {50-57},
      doi = {10.11648/j.acm.20180702.13},
      url = {https://doi.org/10.11648/j.acm.20180702.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180702.13},
      abstract = {One-dimensional parabolic-parabolic Keller-Segel (PP-KS) model of chemotaxis is considered. By using the generalized tanh function method, G'(/G)-expansion method and variable-separating method, plenty of new explicit exact solutions, including travelling wave solutions and non-travelling wave solutions, are obtained for the PP-KS model. Compared to the existing results, more new exact solutions are derived and the obtained solutions all have explicit expressions.},
     year = {2018}
    }
    

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    T1  - New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model
    AU  - Lihua Zhang
    AU  - Lixin Ma
    AU  - Fengsheng Xu
    Y1  - 2018/03/07
    PY  - 2018
    N1  - https://doi.org/10.11648/j.acm.20180702.13
    DO  - 10.11648/j.acm.20180702.13
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    EP  - 57
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20180702.13
    AB  - One-dimensional parabolic-parabolic Keller-Segel (PP-KS) model of chemotaxis is considered. By using the generalized tanh function method, G'(/G)-expansion method and variable-separating method, plenty of new explicit exact solutions, including travelling wave solutions and non-travelling wave solutions, are obtained for the PP-KS model. Compared to the existing results, more new exact solutions are derived and the obtained solutions all have explicit expressions.
    VL  - 7
    IS  - 2
    ER  - 

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Author Information
  • Department of Mathematics, Dezhou University, Dezhou, China

  • Department of Mathematics, Dezhou University, Dezhou, China

  • Department of Mathematics, Dezhou University, Dezhou, China

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