Solving Boussinesq Equation by Bilinear Bӓcklund Transformation

M. Y. Adamu; E. Suleiman

doi:doi:10.11648/j.acm.20130202.13

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Solving Boussinesq Equation by Bilinear Bӓcklund Transformation

M. Y. Adamu, E. Suleiman

Received: 5 April 2013 Accepted: Published: 2 April 2013

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Abstract

In this paper Hirota bilinear method is applied to constructing Backlund transformation of the Boussinesq equation. The bilimear Backlund form are used to obtain the soliton solution of the Boussinesq equation. Also as an application for the bilinear Bӓcklund transformation, new classes of wave solutions to the Boussinesq Equation are computed.

DOI	10.11648/j.acm.20130202.13
Published in	Applied and Computational Mathematics (Volume 2, Issue 2, April 2013)
Page(s)	32-35
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

Boussinesq Equation, Backlund Transformation, Hirota Bilinear Form, Travelling Wave

References

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[2]	J.P. Wu, A bilinear Bäcklund transformation and explicit solutions for a (3 + 1)-dimensional soliton equation, Chin. Phys. Lett. 25 (2008) 4192–4194.
[3]	M.J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981.
[4]	M. Y. Adamu and E. Suleiman, On the Generalized Bilinear Differential Equations, IOSR Journal of Mathematics 3,(2013) (4) 24-30.
[5]	W.X. Ma, T.W. Huang, Y. Zhang, A multiple exp-function method for nonlinear differential equations and its application, Phys. Scr. 82 (2010) 065003.
[6]	R. Hirota (2004) The direct method in soliton theory. Cam-bridge, University, Press.
[7]	W.X. Ma, A. Abdeljabbar, M.G. Asaad, Wronskian and Grammian solutions to a (3 + 1)-dimensional generalized KP equation, Appl. Math. Comput.217 (2011) 8722–8730.
[8]	M. Y. Adamu and E. Suleiman On linear Superposition prin-ciple Applying to Hirota Bilinear Equations, American journal of computational and applied mathematics 3(1) (2013) 8-12.
[9]	Magdy G. Asaad and W.X. Ma,Extended Gram-type Deter-minant, wave and rational solutions to (3+1)-dimensional nonlinear evolition equations,Appl. Math and Comp. 219 (2012), 213-225.
[10]	F.C. You, T.C. Xia, D.Y. Chen, Decomposition of the gene-ralized KP, cKP and mKP and their exact solutions, Phys. Lett. A 372 (2008) 3184–3194.
[11]	A.M. Wazwaz, Multiple-soliton solutions for a (3+1)-dimensional generalized KP equation, Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 491–495.

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APA Style

M. Y. Adamu, E. Suleiman. (2013). Solving Boussinesq Equation by Bilinear Bӓcklund Transformation. Applied and Computational Mathematics, 2(2), 32-35. https://doi.org/10.11648/j.acm.20130202.13

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ACS Style

M. Y. Adamu; E. Suleiman. Solving Boussinesq Equation by Bilinear Bӓcklund Transformation. Appl. Comput. Math. 2013, 2(2), 32-35. doi: 10.11648/j.acm.20130202.13

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AMA Style

M. Y. Adamu, E. Suleiman. Solving Boussinesq Equation by Bilinear Bӓcklund Transformation. Appl Comput Math. 2013;2(2):32-35. doi: 10.11648/j.acm.20130202.13

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@article{10.11648/j.acm.20130202.13,
  author = {M. Y. Adamu and E. Suleiman},
  title = {Solving Boussinesq Equation by Bilinear Bӓcklund Transformation},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {2},
  pages = {32-35},
  doi = {10.11648/j.acm.20130202.13},
  url = {https://doi.org/10.11648/j.acm.20130202.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130202.13},
  abstract = {In this paper Hirota bilinear method is applied to constructing Backlund transformation of the Boussinesq equation. The bilimear Backlund form are used to obtain the soliton solution of the Boussinesq equation. Also as an application for the bilinear Bӓcklund transformation, new classes of wave solutions to the Boussinesq Equation are computed.},
 year = {2013}
}

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TY  - JOUR
T1  - Solving Boussinesq Equation by Bilinear Bӓcklund Transformation
AU  - M. Y. Adamu
AU  - E. Suleiman
Y1  - 2013/04/02
PY  - 2013
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JF  - Applied and Computational Mathematics
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PB  - Science Publishing Group
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AB  - In this paper Hirota bilinear method is applied to constructing Backlund transformation of the Boussinesq equation. The bilimear Backlund form are used to obtain the soliton solution of the Boussinesq equation. Also as an application for the bilinear Bӓcklund transformation, new classes of wave solutions to the Boussinesq Equation are computed.
VL  - 2
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Author Information

M. Y. Adamu

Abubakar Tafawa Balewa University, Bauchi, Nigeria
E. Suleiman

Abubakar Tafawa Balewa University, Bauchi, Nigeria

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APA Style

M. Y. Adamu, E. Suleiman. (2013). Solving Boussinesq Equation by Bilinear Bӓcklund Transformation. Applied and Computational Mathematics, 2(2), 32-35. https://doi.org/10.11648/j.acm.20130202.13

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ACS Style

M. Y. Adamu; E. Suleiman. Solving Boussinesq Equation by Bilinear Bӓcklund Transformation. Appl. Comput. Math. 2013, 2(2), 32-35. doi: 10.11648/j.acm.20130202.13

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AMA Style

M. Y. Adamu, E. Suleiman. Solving Boussinesq Equation by Bilinear Bӓcklund Transformation. Appl Comput Math. 2013;2(2):32-35. doi: 10.11648/j.acm.20130202.13

Copy | Download

@article{10.11648/j.acm.20130202.13,
  author = {M. Y. Adamu and E. Suleiman},
  title = {Solving Boussinesq Equation by Bilinear Bӓcklund Transformation},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {2},
  pages = {32-35},
  doi = {10.11648/j.acm.20130202.13},
  url = {https://doi.org/10.11648/j.acm.20130202.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130202.13},
  abstract = {In this paper Hirota bilinear method is applied to constructing Backlund transformation of the Boussinesq equation. The bilimear Backlund form are used to obtain the soliton solution of the Boussinesq equation. Also as an application for the bilinear Bӓcklund transformation, new classes of wave solutions to the Boussinesq Equation are computed.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Solving Boussinesq Equation by Bilinear Bӓcklund Transformation
AU  - M. Y. Adamu
AU  - E. Suleiman
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130202.13
DO  - 10.11648/j.acm.20130202.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 32
EP  - 35
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130202.13
AB  - In this paper Hirota bilinear method is applied to constructing Backlund transformation of the Boussinesq equation. The bilimear Backlund form are used to obtain the soliton solution of the Boussinesq equation. Also as an application for the bilinear Bӓcklund transformation, new classes of wave solutions to the Boussinesq Equation are computed.
VL  - 2
IS  - 2
ER  -

Copy | Download