The traveling wave solutions for some nonlinear PDEs using the (G'/G)-expansion method

2012 ◽  
Vol 3 (2) ◽  
pp. 39-45
Author(s):  
J.F. Alzaidy
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Pdes ◽  
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 Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2126
Author(s):  
Hammad Alotaibi
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Research Area ◽  
Nonlinear Pdes ◽  
Wave Solutions ◽  
Application Fields ◽  
Diffusion Convection ◽  
Parameter Values

The inspection of wave motion and propagation of diffusion, convection, dispersion, and dissipation is a key research area in mathematics, physics, engineering, and real-time application fields. This article addresses the generalized dimensional Hirota–Maccari equation by using two different methods: the exp(−φ(ζ)) expansion method and Addendum to Kudryashov’s method to obtain the optical traveling wave solutions. By utilizing suitable transformations, the nonlinear pdes are transformed into odes. The traveling wave solutions are expressed in terms of rational functions. For certain parameter values, the obtained optical solutions are described graphically with the aid of Maple 15 software.

On traveling wave solutions: The Wu–Zhang system describing dispersive long waves

2019 ◽  
Vol 33 (06) ◽  
pp. 1950059 ◽  
Author(s):  
A. U. Awan ◽  
M. Tahir ◽  
H. U. Rehman
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Long Waves ◽  
Nonlinear Pdes ◽  
Wave Solutions ◽  
Singular Wave

In this paper, we construct exact families of traveling wave (periodic wave, solitary wave, shock wave, singular-wave, singular-periodic wave, and singular-solitary wave) solutions of a well-known system of nonlinear PDEs, the Wu–Zhang system, which describes (1[Formula: see text]+[Formula: see text]1)-dimensional dispersive long waves. This system is solved by using the generalized [Formula: see text] expansion method, where G satisfies the Jacobi elliptic equation of fourth order. Meanwhile, the mechanical features of some families are explained through three-dimensional figures.

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.

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