Enhanced (G^/G)-Expansion Method to Find the Exact Complexiton Soliton Solutions of (3+1)-Dimensional Zakhrov-Kuznetsov Equation

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Enhanced (G^/G)-Expansion Method to Find the Exact Complexiton Soliton Solutions of (3+1)-Dimensional Zakhrov-Kuznetsov Equation

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Abstract

In this article, an enhanced (𝐺𝐺 β€² /𝐺𝐺)-expansion method has been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation. The efficiency of this method for finding these exact solutions has been demonstrated. As a result, a set of complexiton soliton solutions are derived, which are expressed by the combinations of rational, hyperbolic and trigonometric functions involving several parameters. It is shown that the method is effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics.

References

37 Cites in Article
  1. 1. R Hirota (1973). Exact envelope soliton solutions of a nonlinear wave equation. J. Math. Phy, 14, 805-810.
  2. 2. Ryogo Hirota,Junkichi Satsuma (1981). Soliton solutions of a coupled Korteweg-de Vries equation. Physics Letters A, 85(8-9), 407-408.
  3. 3. M Malfliet (1992). Solitary wave solutions of nonlinear wave equations. Am. J. Phys, 60, 650-654.
  4. 4. H Nassar,M Abdel-Razek,A Seddeek (2011). Expanding the tanh-function method for solving nonlinear equations. Appl. Math, 2, 1096-1104.
  5. 5. Engui Fan (2000). Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277(4-5), 212-218.
  6. 6. M Abdou (2007). The extended tanh method and its applications for solving nonlinear physical models. Applied Mathematics and Computation, 190(1), 988-996.
  7. 7. J He,X Wu (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons and Fract, 30, 700-708.
  8. 8. M Akbar,N Ali (2011). Exp-function method for Duffing Equation and new solutions of (2+1) dimensional dispersive long wave equations. Prog. Appl. Math, 1(2), 30-42.
  9. 9. H Naher,A Abdullah,M Akbar (2011). The Exp-function method for new exact solutions of the nonlinear partial differential equations. Int. J. Phys. Sci, 6(29), 6706-6716.
  10. 10. H Naher,A Abdullah,M Akbar New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method. J. Appl. Math., Article ID, 14.
  11. 11. A Bekir,A Boz (2008). Exact solutions for nonlinear evolution equations using Expfunction method. Phy. Lett. A, 372, 1619-1625.
  12. 12. M Abdou,A Soliman,S El-Basyony (2007). New application of Exp-function method for improved Boussinesq equation. Physics Letters A, 369(5-6), 469-475.
  13. 13. S El-Wakil,M Madkour,M Abdou (2007). Application of Exp-function method for nonlinear evolution equations with variable coefficients. Physics Letters A, 369(1-2), 62-69.
  14. 14. Syed Mohyud-Din,Muhammad Noor,Asif Waheed (2010). Exp-Function Method for Generalized Travelling Solutions of Calogero-Degasperis-Fokas Equation. Zeitschrift fΓΌr Naturforschung A, 65(1-2), 78-84.
  15. 15. G Adomian (1994). Solving frontier problems of physics: The decomposition method. Solving frontier problems of physics: The decomposition method
  16. 16. Y Zhou,M Wang,Y Wang (2003). Periodic wave solutions to coupled KdV equations with variable coefficients. Phys. Lett. A, 308, 31-36.
  17. 17. Sirendaoreji (2004). New exact travelling wave solutions for the Kawahara and modified Kawahara equations. Chaos Solitons Fract, 19, 147-150.
  18. 18. A Ali (2011). New generalized Jacobi elliptic function rational expansion method. J. Comput. Appl. Math, 235, 4117-4127.
  19. 19. Y He,S Li,Y Long (2012). Exact solutions of the Klein-Gordon equation by modified Expfunction method. Int. Math. Forum, 7(4), 175-182.
  20. 20. M Akbar,Norhashidah Ali,E Zayed (2012). Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved ( G β€²/ G )-Expansion Method. Communications in Theoretical Physics, 57(2), 173-178.
  21. 21. Mingliang Wang (1995). Solitary wave solutions for variant Boussinesq equations. Physics Letters A, 199(3-4), 169-172.
  22. 22. E Zayed,H Zedan,K Gepreel (2004). On the solitary wave solutions for nonlinear Hirota-Sasuma coupled KDV equations. Chaos, Solitons and Fractals, 22, 285-303.
  23. 23. A Jawad,M Petkovic,A Biswas (2010). Modified simple equation method for nonlinear evolution equations. Appl. Math. Comput, 217, 869-877.
  24. 24. E Zayed (2011). A note on the modified simple equation method applied to Sharma-Tasso-Olver equation. Appl. Math. Comput, 218, 3962-3964.
  25. 25. E Zayed,S Ibrahim (2012). Exact solutions of nonlinear evolution equations in Mathematical physics using the modified simple equation method. Chinese Phys. Lett, 29(6), 60201.
  26. 26. K Khan,M Akbar,N Ali The Modified Simple Equation Method for Exact and Solitary Wave Solutions of Nonlinear Evolution Equation: The GZK-BBM Equation and Right-Handed Noncommutative Burgers Equations. ISRN Mathematical Physics, 2013
  27. 27. Kamruzzaman Khan,M Akbar (2013). Exact and solitary wave solutions for the Tzitzeica–Dodd–Bullough and the modified KdV–Zakharov–Kuznetsov equations using the modified simple equation method. Ain Shams Engineering Journal, 4(4), 903-909.
  28. 28. S Mohyud-Din,M Noor,K Noor (2009). Travelling wave solutions of seventhorder generalized KdV equations using He's polynomials. International Journal of Nonlinear Sciences and Numerical Simulation, 10(2), 223-229.
  29. 29. J He (2008). An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int. J. Mod. Phys. B, 22(21), 3487-3578.
  30. 30. Syed Mohyud-Din,Muhammad Noor,Khalida Noor (2009). Some Relatively New Techniques for Nonlinear Problems. Mathematical Problems in Engineering, 2009(1)
  31. 31. S Mohyud-Din,M Noor,K Noor,M Hosseini (2010). Solution of singular equations by He's variational iteration method. International Journal of Nonlinear Sciences and Numerical Simulation, 11(2), 81-86.
  32. 32. W Ma,Y You (2004). Rational solutions of the Toda lattice equation in Casoratian form. Chaos, Solitons & Fractals, 22, 395-406.
  33. 33. Wen-Xiu Ma,Hongyou Wu,Jingsong He (2007). Partial differential equations possessing Frobenius integrable decompositions. Physics Letters A, 364(1), 29-32.
  34. 34. K Gepreel,A Shehata Exact complexiton soliton solutions for nonlinear partial differential equations in mathematical physics. Scientific Research and Essays, 7(2), 149-157.
  35. 35. K Gepreel (2011). Exact Solutions of Nonlinear Partial Differential Equations. Handbook of Nonlinear Partial Differential Equations, Second Edition, 6, 1-2.
  36. 36. Kamruzzaman Khan,M Ali Akbar (2014). Traveling wave solutions of nonlinear evolution equations via the enhanced (Gβ€²/G)-expansion method. Journal of the Egyptian Mathematical Society, 22(2), 220-226.
  37. 37. G,/ Unknown Title.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Kamruzzaman Khan, Rafiqul Islam, Ekramul Islam, Dr.. 2013. "Enhanced (G^/G)-Expansion Method to Find the Exact Complexiton Soliton Solutions of (3+1)-Dimensional Zakhrov-Kuznetsov Equation". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue F8).

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Classification
GJSFR-F Classification MSC 2010: 13D02
Version of record

v1.2

Issue date
October 6, 2013

Language
English
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Enhanced (G^/G)-Expansion Method to Find the Exact Complexiton Soliton Solutions of (3+1)-Dimensional Zakhrov-Kuznetsov Equation

Kamruzzaman Khan
Kamruzzaman Khan Pabna University of Science and Technology
Rafiqul Islam
Rafiqul Islam <p>Pabna University of Science and Technology</p>
Ekramul Islam
Ekramul Islam <p>Pabna University of Science and Technology</p>
<p>Pabna University of Science and Technology</p>