Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water

Baodan Tian; Yanhong Qiu

doi:doi:10.11648/j.pamj.20160506.11

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Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water

Baodan Tian, Yanhong Qiu

Received: 2 September 2016 Accepted: 18 September 2016 Published: 17 October 2016

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Abstract

In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.

DOI	10.11648/j.pamj.20160506.11
Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 6, December 2016)
Page(s)	174-180
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), 2024. Published by Science Publishing Group

Keywords

Whitham-Broer-Kaup Equations, Direct Method, Equivalence Transformation, Symmetry, Explicit Solutions

References

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Baodan Tian, Yanhong Qiu. (2016). Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water. Pure and Applied Mathematics Journal, 5(6), 174-180. https://doi.org/10.11648/j.pamj.20160506.11

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ACS Style

Baodan Tian; Yanhong Qiu. Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water. Pure Appl. Math. J. 2016, 5(6), 174-180. doi: 10.11648/j.pamj.20160506.11

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AMA Style

Baodan Tian, Yanhong Qiu. Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water. Pure Appl Math J. 2016;5(6):174-180. doi: 10.11648/j.pamj.20160506.11

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@article{10.11648/j.pamj.20160506.11,
  author = {Baodan Tian and Yanhong Qiu},
  title = {Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {6},
  pages = {174-180},
  doi = {10.11648/j.pamj.20160506.11},
  url = {https://doi.org/10.11648/j.pamj.20160506.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160506.11},
  abstract = {In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.},
 year = {2016}
}

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TY  - JOUR
T1  - Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water
AU  - Baodan Tian
AU  - Yanhong Qiu
Y1  - 2016/10/17
PY  - 2016
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DO  - 10.11648/j.pamj.20160506.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 174
EP  - 180
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160506.11
AB  - In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.
VL  - 5
IS  - 6
ER  -

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Author Information

Baodan Tian

School of science, Southwest University of Science and Technology, Mianyang, China
Yanhong Qiu

School of science, Southwest University of Science and Technology, Mianyang, China

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APA Style

Baodan Tian, Yanhong Qiu. (2016). Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water. Pure and Applied Mathematics Journal, 5(6), 174-180. https://doi.org/10.11648/j.pamj.20160506.11

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ACS Style

Baodan Tian; Yanhong Qiu. Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water. Pure Appl. Math. J. 2016, 5(6), 174-180. doi: 10.11648/j.pamj.20160506.11

Copy | Download

AMA Style

Baodan Tian, Yanhong Qiu. Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water. Pure Appl Math J. 2016;5(6):174-180. doi: 10.11648/j.pamj.20160506.11

Copy | Download

@article{10.11648/j.pamj.20160506.11,
  author = {Baodan Tian and Yanhong Qiu},
  title = {Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {6},
  pages = {174-180},
  doi = {10.11648/j.pamj.20160506.11},
  url = {https://doi.org/10.11648/j.pamj.20160506.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160506.11},
  abstract = {In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water
AU  - Baodan Tian
AU  - Yanhong Qiu
Y1  - 2016/10/17
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160506.11
DO  - 10.11648/j.pamj.20160506.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 174
EP  - 180
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160506.11
AB  - In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.
VL  - 5
IS  - 6
ER  -

Copy | Download