Exact Traveling Wave Solutions for the (2+1)-Dimensional ZK-BBM Equation by Exp )) ( ( i i i-Expansion Method

Harun-Or-Roshid; Md. Nur Alam

Authors

Harun-Or-Roshid
Md. Nur Alam

the exp(−Φ(η)) -expansion method; the (2 1)-dimensional ZK-BBM equation; complixiton soliton solutions; traveling wave solutions; solitary wave so

Abstract

In this work, the exp(-Φ(η)) -expansion method is applied to solve the (2+1)dimensional ZK-BBM equation. The traveling wave solutions are expressed in terms of the exponential functions, the hyperbolic functions, the trigonometric functions and the rational functions. The procedure is simple, direct and constructive without the help of a computer algebra system. The exp(-Φ(η)) -expansion method will be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in mathematical physics and engineering.

Downloads

How to Cite

Exact Traveling Wave Solutions for the (2+1)-Dimensional ZK-BBM Equation by Exp )) ( ( i i i-Expansion Method. (2014). Global Journal of Science Frontier Research, 14(A2), 1-5. https://www.journalofscience.org/index.php/GJSFR/article/view/100536

Download Citation

References

E Zayed, A Abourabia, Khaled Gepreel, M Horbaty (2006) On the rational solitary wave solutions for the nonlinear Hirota-Satsuma coupled KdV system. 85(6-7), 751-768.

K Chow (1995) A class of exact periodic solutions of nonlinear envelope equation. 36, 4125-4137.

D Liu (2005) Jacobi elliptic function solutions for two variant Boussinesq equations. 24, 1373-1385.

Y Chen, Q Wang (2005) Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic functions solutions to (1+1)-dimensional dispersive long wave equation. 24, 745-757.

M Wang, Y Zhou (2003) The periodic wave solutions for the Klein-Gordon-Schrodinger equations. 318, 84-92.

M Wang, X Li (2005) Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations. 343, 48-54.

Mingliang Wang, Xiangzheng Li, Jinliang Zhang (2008) The ()-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. 372(4), 417-423.

R Gupta, S Kumar, B Lai (2012) New exact traveling wave solutions of generalized sinh-Gordon and the (2+1)-dimensional ZK-BBM equations. 6(03), 344-355.

Md. Alam, Md. Akbar, Syed Mohyud-Din (2014) A novel (G′/G)-expansion method and its application to the Boussinesq equation. 23(2), 020203.

M Alam, M Akbar (2013) Exact traveling wave solutions of the KP-BBM equation by using the new generalized (G′/G) -expansion method. 2(1), 617.

Ahmet Bekir (2008) Application of the -expansion method for nonlinear evolution equations. 372(19), 3400-3406.

Harun-Or- Roshid, M Akbar, Md Alam, Md Hoque, Nizhum Rahman (2014) New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation. 3(1), 122.

Md Alam, M Akbar, Harun-Or- Roshid (2014) Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G′/G)-expansion method. 3(1), 43.

Md. Alam, M Akbar (2014) Application of the new approach of generalized (G' /G) -expansion method to find exact solutions of nonlinear PDEs in mathematical physics. 10, 58-70.

Md Alam, M Akbar (2013) Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G′/G)-expansion method. 2(1), 500-523.

R Hirota (2004) The direct method in soliton theory.

M Miura (1978) Backlund transformation.

Vladimir Matveev, Mikhail Salle (1991) Darboux Transformations and Solitons.

Syed Mohyud-Din, Muhammad Noor (2007) Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems. 2007(15), 1-15.

Syed Mohyud-Din, Muhammad Noor (2009) Homotopy Perturbation Method for Solving Partial Differential Equations. 64(3-4), 157-170.

N Rahman, H Roshid, M Alam, S Zafor (2014) Traveling Wave Solutions of The (1+1)-Dimensional Compound KdVB equation by Exp(-Φ(η )) -Expansion Method. 3(2), 93-97.

N Rahman, S Akter, H Roshid, M Alam (2014) Traveling Wave Solutions of The (1+1)-Dimensional Compound KdVB equation by Exp (-Φ(η )) -Expansion Method. 13(8), 7-13.

R Islam, M Alam, A Hossain, H Roshid, M Akbar (2014) Traveling wave solutions of nonlinear evolution equations via exp (-Φ(η))expansion method. 13(11), 63-71.

N Rahman, M Alam, H Roshid, S Akter, M Akbar (2014) Application of exp (-Φ(η)) -expansion method to find the exact solutions of Shorma-Tasso-Olver equation. 7(1), 1-6.

M Uddin, M Alam, S Hossain, M Hasan, M Akbar (2014) Some new exact traveling wave solutions to the (3+1)-dimensional Zakharov-Kuznetsov equation and the Burgers equations via Exp (-Φ(η)) -Expansion Method. 1(1), 1-8.