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

Kamruzzaman Khan; Rafiqul Islam; Ekramul Islam

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

Kamruzzaman Khan * § Ph.D.

Contact

Rafiqul Islam

Contact

Ekramul Islam

Contact

§ Pabna University of Science and Technology

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

Article Fingerprint

ReserarchID

D1XIU

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

AI TAKEAWAY

Connecting with the Eternal Ground

Abstract

In this article, an enhanced (𝐺𝐺 ′ /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

Reference Format

R Hirota (1973). Exact envelope soliton solutions of a nonlinear wave equation.
Ryogo Hirota,Junkichi Satsuma (1981). Soliton solutions of a coupled Korteweg-de Vries equation.
M Malfliet (1992). Solitary wave solutions of nonlinear wave equations.
H Nassar,M Abdel-Razek,A Seddeek (2011). Expanding the tanh-function method for solving nonlinear equations.
Engui Fan (2000). Extended tanh-function method and its applications to nonlinear equations.
M Abdou (2007). The extended tanh method and its applications for solving nonlinear physical models.
J He,X Wu (2006). Exp-function method for nonlinear wave equations.
M Akbar,N Ali (2011). Exp-function method for Duffing Equation and new solutions of (2+1) dimensional dispersive long wave equations.
H Naher,A Abdullah,M Akbar (2011). The Exp-function method for new exact solutions of the nonlinear partial differential equations.
H Naher,A Abdullah,M Akbar New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method.
A Bekir,A Boz (2008). Exact solutions for nonlinear evolution equations using Expfunction method.
M Abdou,A Soliman,S El-Basyony (2007). New application of Exp-function method for improved Boussinesq equation.
S El-Wakil,M Madkour,M Abdou (2007). Application of Exp-function method for nonlinear evolution equations with variable coefficients.
Syed Mohyud-Din,Muhammad Noor,Asif Waheed (2010). Exp-Function Method for Generalized Travelling Solutions of Calogero-Degasperis-Fokas Equation.
G Adomian (1994). Solving frontier problems of physics: The decomposition method.
Y Zhou,M Wang,Y Wang (2003). Periodic wave solutions to coupled KdV equations with variable coefficients.
Sirendaoreji (2004). New exact travelling wave solutions for the Kawahara and modified Kawahara equations.
A Ali (2011). New generalized Jacobi elliptic function rational expansion method.
Y He,S Li,Y Long (2012). Exact solutions of the Klein-Gordon equation by modified Expfunction method.
M Akbar,Norhashidah Ali,E Zayed (2012). Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved ( <i>G</i> ′/ <i>G</i> )-Expansion Method.
Mingliang Wang (1995). Solitary wave solutions for variant Boussinesq equations.
E Zayed,H Zedan,K Gepreel (2004). On the solitary wave solutions for nonlinear Hirota-Sasuma coupled KDV equations.
A Jawad,M Petkovic,A Biswas (2010). Modified simple equation method for nonlinear evolution equations.
E Zayed (2011). A note on the modified simple equation method applied to Sharma-Tasso-Olver equation.
E Zayed,S Ibrahim (2012). Exact solutions of nonlinear evolution equations in Mathematical physics using the modified simple equation method.
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.
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.
S Mohyud-Din,M Noor,K Noor (2009). Travelling wave solutions of seventhorder generalized KdV equations using He's polynomials.
J He (2008). An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering.
Syed Mohyud-Din,Muhammad Noor,Khalida Noor (2009). Some Relatively New Techniques for Nonlinear Problems.
S Mohyud-Din,M Noor,K Noor,M Hosseini (2010). Solution of singular equations by He's variational iteration method.
W Ma,Y You (2004). Rational solutions of the Toda lattice equation in Casoratian form.
Wen-Xiu Ma,Hongyou Wu,Jingsong He (2007). Partial differential equations possessing Frobenius integrable decompositions.
K Gepreel,A Shehata Exact complexiton soliton solutions for nonlinear partial differential equations in mathematical physics.
K Gepreel (2011). Exact Solutions of Nonlinear Partial Differential Equations.
Kamruzzaman Khan,M Ali Akbar (2014). Traveling wave solutions of nonlinear evolution equations via the enhanced (G′/G)-expansion method.
G,/ Unknown Title.

Download References

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. 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, Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue F8).

More Citation Formats

Select Citation Style:

Download Citation

GJSFR Volume 13 Issue F8

Explore Journals Explore Volume Read This Issue

Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

complexiton soliton solutions enhanced 􁈺􀜩􀔢􀈀􀜩􁈻-expansion method traveling wave solutions zk equation

Classification

GJSFR-F Classification MSC 2010: 13D02

Submission ReceivedAugust 16, 2013
Peer Review Double Blind
Handling Editor
Accepted September 7, 2013
Published September 22, 2013

Version of record

v1.2

Issue date

October 6, 2013

Language

English

Experiance in AR

Explore published articles in an immersive Augmented Reality environment. Our platform converts research papers into interactive 3D books, allowing readers to view and interact with content using AR and VR compatible devices.

View in VR

Read in 3D

Your published article is automatically converted into a realistic 3D book. Flip through pages and read research papers in a more engaging and interactive format.

View in 3D

Article Matrices

Total Score: 148

Country: Bangladesh

Subject: Global Journal of Science Frontier Research

Authors: Rafiqul Islam, Kamruzzaman Khan, M. Ali Akbar, Ekramul Islam (PhD/Dr. count: 0)

View Count (all-time): 240

Total Views (Real + Logic): 1109

Total Downloads (simulated): 84

Publish Date: 2013 09, Sun

Monthly Totals (Real + Logic):

Month 1: 43 views
Month 2: 55 views
Month 3: 52 views
Month 4: 53 views
Month 5: 54 views
Month 6: 31 views
Month 7: 20 views
Month 8: 26 views
Month 9: 34 views
Month 10: 41 views
Month 11: 58 views
Month 12: 38 views
Month 13: 44 views
Month 14: 27 views
Month 15: 45 views
Month 16: 34 views
Month 17: 28 views
Month 18: 20 views
Month 19: 34 views
Month 20: 19 views
Month 21: 45 views
Month 22: 37 views
Month 23: 24 views
Month 24: 25 views
Month 25: 20 views
Month 26: 32 views
Month 27: 28 views
Month 28: 12 views
Month 29: 23 views
Month 30: 12 views
Month 31: 24 views
Month 32: 24 views
Month 33: 43 views
Month 34: 40 views
Month 35: 18 views
Month 36: 19 views
Month 37: 46 views
Month 38: 39 views
Month 39: 41 views
Month 40: 21 views
Month 41: 36 views
Month 42: 33 views
Month 43: 29 views
Month 44: 30 views
Month 45: 44 views
Month 46: 24 views
Month 47: 28 views
Month 48: 41 views
Month 49: 39 views
Month 50: 10 views
Month 51: 38 views
Month 52: 31 views
Month 53: 20 views
Month 54: 24 views
Month 55: 27 views
Month 56: 20 views
Month 57: 17 views
Month 58: 21 views
Month 59: 25 views
Month 60: 40 views
Month 61: 34 views
Month 62: 36 views
Month 63: 49 views
Month 64: 18 views
Month 65: 29 views
Month 66: 40 views
Month 67: 26 views
Month 68: 27 views
Month 69: 26 views
Month 70: 16 views
Month 71: 44 views
Month 72: 31 views
Month 73: 26 views
Month 74: 31 views
Month 75: 49 views
Month 76: 31 views
Month 77: 25 views
Month 78: 32 views
Month 79: 37 views
Month 80: 35 views
Month 81: 50 views
Month 82: 24 views
Month 83: 23 views
Month 84: 29 views
Month 85: 30 views
Month 86: 22 views
Month 87: 29 views
Month 88: 14 views
Month 89: 22 views
Month 90: 31 views
Month 91: 39 views
Month 92: 17 views
Month 93: 46 views
Month 94: 32 views
Month 95: 20 views
Month 96: 14 views
Month 97: 23 views
Month 98: 24 views
Month 99: 32 views
Month 100: 40 views
Month 101: 35 views
Month 102: 35 views
Month 103: 25 views
Month 104: 43 views
Month 105: 30 views
Month 106: 24 views
Month 107: 17 views
Month 108: 26 views
Month 109: 44 views
Month 110: 20 views
Month 111: 20 views
Month 112: 41 views
Month 113: 40 views
Month 114: 29 views
Month 115: 31 views
Month 116: 35 views
Month 117: 39 views
Month 118: 13 views
Month 119: 43 views
Month 120: 14 views
Month 121: 16 views
Month 122: 30 views
Month 123: 43 views
Month 124: 41 views
Month 125: 32 views
Month 126: 30 views
Month 127: 17 views
Month 128: 36 views
Month 129: 42 views
Month 130: 34 views
Month 131: 27 views
Month 132: 35 views
Month 133: 36 views
Month 134: 34 views
Month 135: 28 views
Month 136: 24 views
Month 137: 23 views
Month 138: 18 views
Month 139: 40 views
Month 140: 31 views
Month 141: 17 views
Month 142: 29 views
Month 143: 24 views
Month 144: 36 views
Month 145: 42 views
Month 146: 26 views
Month 147: 33 views
Month 148: 42 views
Month 149: 39 views
Month 150: 57 views
Month 151: 56 views
Month 152: 41 views
Month 153: 35 views
Month 154: 40 views
Month 155: 39 views
Month 156: 44 views

Total Views: 1.1K

Total Downloads: 84

All Trends