Applied and Computational Mathematics

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

Received: Jan. 30, 2018    Accepted: Feb. 11, 2018    Published: Mar. 07, 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.

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

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

References
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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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    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://download.sciencepg.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
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    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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