The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method

Sen-Yung Lee; Chun-Ku Kuo

doi:doi:10.11648/j.acm.20150405.11

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The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method

Sen-Yung Lee, Chun-Ku Kuo

Published in Applied and Computational Mathematics (Volume 4, Issue 5)

Received: 29 June 2015 Accepted: 5 August 2015 Published: 19 August 2015

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Abstract

The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed.

Published in	Applied and Computational Mathematics (Volume 4, Issue 5)
DOI	10.11648/j.acm.20150405.11
Page(s)	335-341
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), 2015. Published by Science Publishing Group

Keywords

General Form, Linearized, KdV, Simplest Equation Method, Bernoulli, Discontinuity, Soliton Sliding

References

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[13]	Wang, M, Wang, Y, Yubin, Z. An auto-Backlund transformation and exact solutions to a generalized KdV equation with variable coefficients and their applications. Physics Letter A 303, 45-51 (2002)
[14]	Kudryashov, NA. One method for finding exact solutions of nonlinear differential equations. Commun Nonlinear Sci Numer Simulat 17, 2248-2253 (2012)
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Sen-Yung Lee, Chun-Ku Kuo. (2015). The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method. Applied and Computational Mathematics, 4(5), 335-341. https://doi.org/10.11648/j.acm.20150405.11

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ACS Style

Sen-Yung Lee; Chun-Ku Kuo. The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method. Appl. Comput. Math. 2015, 4(5), 335-341. doi: 10.11648/j.acm.20150405.11

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AMA Style

Sen-Yung Lee, Chun-Ku Kuo. The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method. Appl Comput Math. 2015;4(5):335-341. doi: 10.11648/j.acm.20150405.11

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@article{10.11648/j.acm.20150405.11,
  author = {Sen-Yung Lee and Chun-Ku Kuo},
  title = {The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {5},
  pages = {335-341},
  doi = {10.11648/j.acm.20150405.11},
  url = {https://doi.org/10.11648/j.acm.20150405.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150405.11},
  abstract = {The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed.},
 year = {2015}
}

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TY  - JOUR
T1  - The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method
AU  - Sen-Yung Lee
AU  - Chun-Ku Kuo
Y1  - 2015/08/19
PY  - 2015
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DO  - 10.11648/j.acm.20150405.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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EP  - 341
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150405.11
AB  - The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed.
VL  - 4
IS  - 5
ER  -

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Author Information

Sen-Yung Lee

Department of Mechanical Engineering, National Cheng Kung University, Taiwan, R.O.C.
Chun-Ku Kuo

Department of Mechanical Engineering, Air Force Institute of Technology, Taiwan, R.O.C.

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APA Style

Sen-Yung Lee, Chun-Ku Kuo. (2015). The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method. Applied and Computational Mathematics, 4(5), 335-341. https://doi.org/10.11648/j.acm.20150405.11

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ACS Style

Sen-Yung Lee; Chun-Ku Kuo. The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method. Appl. Comput. Math. 2015, 4(5), 335-341. doi: 10.11648/j.acm.20150405.11

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AMA Style

Sen-Yung Lee, Chun-Ku Kuo. The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method. Appl Comput Math. 2015;4(5):335-341. doi: 10.11648/j.acm.20150405.11

Copy | Download

@article{10.11648/j.acm.20150405.11,
  author = {Sen-Yung Lee and Chun-Ku Kuo},
  title = {The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {5},
  pages = {335-341},
  doi = {10.11648/j.acm.20150405.11},
  url = {https://doi.org/10.11648/j.acm.20150405.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150405.11},
  abstract = {The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method
AU  - Sen-Yung Lee
AU  - Chun-Ku Kuo
Y1  - 2015/08/19
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150405.11
DO  - 10.11648/j.acm.20150405.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 335
EP  - 341
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150405.11
AB  - The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed.
VL  - 4
IS  - 5
ER  -

Copy | Download