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

Lihua Zhang; Lixin Ma; Fengsheng Xu

doi:doi:10.11648/j.acm.20180702.13

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

Lihua Zhang, Lixin Ma, Fengsheng Xu

Published in Applied and Computational Mathematics (Volume 7, Issue 2)

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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TY  - JOUR
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
SP  - 50
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

Lihua Zhang

Department of Mathematics, Dezhou University, Dezhou, China
Lixin Ma

Department of Mathematics, Dezhou University, Dezhou, China
Fengsheng Xu

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
SP  - 50
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  -

Copy | Download