Research Article

SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION

Volume: 3 Number: 2 October 1, 2015
EN

SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION

Abstract

In present paper, the seventh-order KdV types of equation is considered by the Lie symmetry analysis. All of the geometric vector elds of the KdV equation are obtained, then the symmetry reductions and exact solutions to the KdV equation are investigated by the dynamical system and the power series method.

Keywords

References

  1. [1] M. Craddock, K. Lennox, Lie group symmetries as integral transforms of fundamental solutions, J. Differential Equations, 232 (2007), 652-674.
  2. [2] F. Gungor, C.  Ozemir, Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khokhlov equation, J. Math. Anal. Appl., 423 (2015), 623-638.
  3. [3] M. Lakshmanan, P. Kaliappan, Lie transformations, nonlinear evolution equations and Painleve forms, J. Math. Phys., 24 (1983), 795-806.
  4. [4] H. Liu, J. Li, Lie symmetry analysis and exact solutions for the extended mKdV equation, Acta Appl. Math., 109 (2010), 1107-1119.
  5. [5] H. Liu, J. Li, F. Chen, Exact periodic wave solutions for the hKdV equation, Nonlinear Anal., 70 (2009), 2376-2381.
  6. [6] H. Liu, J. Li, L. Liu, Lie symmetry analysis, optimal systems and exact solutions to the fth-order KdV types of equations, J. Math. Anal. Appl., 368 (2010), 551-558.
  7. [7] H. Liu, J. Li, L. Liu, Conservation law classi cation and integrability of generalized nonlinear second-order equation, Commun. Theor. Phys. (Beijing), 56 (2011), 987-991.
  8. [8] H. Liu, Y. Geng, Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying uid, J. Differential Equations, 254 (2013), 2289-2303.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Publication Date

October 1, 2015

Submission Date

July 10, 2014

Acceptance Date

-

Published in Issue

Year 2015 Volume: 3 Number: 2

APA
Zhang, Y. (2015). SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp Journal of Mathematics, 3(2), 122-130. https://izlik.org/JA53UF46MT
AMA
1.Zhang Y. SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp J. Math. 2015;3(2):122-130. https://izlik.org/JA53UF46MT
Chicago
Zhang, Youwei. 2015. “SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION”. Konuralp Journal of Mathematics 3 (2): 122-30. https://izlik.org/JA53UF46MT.
EndNote
Zhang Y (October 1, 2015) SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp Journal of Mathematics 3 2 122–130.
IEEE
[1]Y. Zhang, “SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION”, Konuralp J. Math., vol. 3, no. 2, pp. 122–130, Oct. 2015, [Online]. Available: https://izlik.org/JA53UF46MT
ISNAD
Zhang, Youwei. “SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION”. Konuralp Journal of Mathematics 3/2 (October 1, 2015): 122-130. https://izlik.org/JA53UF46MT.
JAMA
1.Zhang Y. SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp J. Math. 2015;3:122–130.
MLA
Zhang, Youwei. “SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION”. Konuralp Journal of Mathematics, vol. 3, no. 2, Oct. 2015, pp. 122-30, https://izlik.org/JA53UF46MT.
Vancouver
1.Youwei Zhang. SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp J. Math. [Internet]. 2015 Oct. 1;3(2):122-30. Available from: https://izlik.org/JA53UF46MT
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.