New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model
Applied and Computational Mathematics
Volume 7, Issue 2, April 2018, Pages: 50-57
Received: Jan. 30, 2018; Accepted: Feb. 11, 2018; Published: Mar. 7, 2018
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Authors
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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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.
Keywords
Keller-Segel Model, Generalized Tanh Function Method, (G'/G)-Expansion Method, Variable-Separating Method, Exact Solutions
To cite this article
Lihua Zhang, Lixin Ma, Fengsheng Xu, New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model, Applied and Computational Mathematics. Vol. 7, No. 2, 2018, pp. 50-57. doi: 10.11648/j.acm.20180702.13
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Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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