The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
By Mingliang Wang, Xiangzheng Li, Jinliang Zhang. 2008
2,060 citations recorded by the source corpus.
The (G'/G)-expansion method is firstly proposed, where G = G(xi) satisfies a second order linear ordinary differential equation (LODE for short), by which the travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations and the Hirota-Satsuma equations are obtained. When the parameters are taken as special values the solitary waves are also derived from the travelling waves. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The proposed method is direct, concise, elementary and effective, and can be used for many other nonlinear evolution equations. (C) 2007 Published by Elsevier B.V.
Subfields: Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d1bf87a515b0fd410cfda10a308920d72b6d92ac
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In Modeling and Simulation
- Hasan Bulut
- M. Osman
- Seyma Tuluce Demiray
- Farah Aini Abdullah
- Y. Pandır
- H. I. Abdel-Gawad
- Erqiang Li
- Hasibun Naher
In Statistical and Nonlinear Physics
- Hasan Bulut
- M. Osman
- Seyma Tuluce Demiray
- Farah Aini Abdullah
- Y. Pandır
- H. I. Abdel-Gawad
- Erqiang Li
- Hasibun Naher
Citations in the corpus
- The (G′/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations (2010, methodology): “Many effective approaches for obtaining exact solutions of NLEEs have been presented, such as the tanh-function expansion method [7], the Jocobi elliptic function expansion method [5], the homogeneous balance method [10], F-expansion method [11], the sub-ODE method [12], the exp-function expansion m”
- All exact travelling wave solutions of Hirota equation and Hirota–Maccari system (2016, background): “In recent years, most authors have enhanced a number of methods to procure exact solutions of NLEEs such as G’/G-expansion method [1, 2], exp-function 10”