scholarly journals Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G′/G)-expansion method

SpringerPlus ◽  
2014 ◽  
Vol 3 (1) ◽  
Author(s):  
Md Nur Alam ◽  
M Ali Akbar ◽  
Harun-Or- Roshid
Keyword(s):  
Traveling Wave ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
New Approach ◽  
Wave Solutions

scholarly journals Application of the new approach of generalized (G' /G) -expansion method to find exact solutions of nonlinear PDEs in mathematical physics

BIBECHANA ◽  
2013 ◽  
Vol 10 ◽  
pp. 58-70 ◽  
Author(s):  
Md. Nur Alam ◽  
M Ali Akbar
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Pdes ◽  
Mathematical Tool ◽  
New Approach ◽  
Wave Solutions

The exact solutions of nonlinear evolution equations (NLEEs) play a crucial role to make known the internal mechanism of complex physical phenomena. In this article, we construct the traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation by means of the new approach of generalized (G′ /G) -expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G′ /G) -expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations. BIBECHANA 10 (2014) 58-70 DOI: http://dx.doi.org/10.3126/bibechana.v10i0.9312

scholarly journals Exact Solutions to the (2+1)-Dimensional Boussinesq Equation via exp(?(?))-Expansion Method

2015 ◽  
Vol 7 (3) ◽  
pp. 1-10 ◽  
Author(s):  
M. N. Alam ◽  
M. G. Hafez ◽  
M. A. Akbar ◽  
H. -O. -Roshid
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Boussinesq Equation ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions

The exp(?(?))-expansion method is applied to find exact traveling wave solutions to the (2+1)-dimensional Boussinesq equation which is an important equation in mathematical physics. 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 applied method will be used in further works to establish more new solutions for other kinds of nonlinear evolution equations arising in mathematical physics and engineering.

scholarly journals Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (G′/G)-Expansion Method

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah
Keyword(s):  
Diffusion Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Expansion Method ◽  
Reaction Diffusion Equation ◽  
Wave Solutions ◽  
Nonlinear Reaction ◽  
Nonlinear Reaction Diffusion Equation ◽  
Constant Coefficients

We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G′/G)-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.

Sign in / Sign up

Export Citation Format

Share Document