Some applications of the (G′/G, 1/G)-expansion method to find new exact solutions of NLEEs

• Published in: European physical journal plus Vol. 132; no. 6; p. 252
• Main Authors: Mamun Miah, M., Shahadat Ali, H. M., Ali Akbar, M., Majid Wazwaz, Abdul
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2017; Springer Nature B.V
• Subjects: Algebra; Applied and Technical Physics; Applied mathematics; Atomic; Boussinesq equations; Complex Systems; Condensed Matter Physics; Exact solutions; Hyperbolic functions; Lie groups; Mathematical analysis; Mathematical and Computational Physics; Molecular; Nonlinear differential equations; Nonlinear evolution equations; Optical and Plasma Physics; Ordinary differential equations; Physics; Physics and Astronomy; Rational functions; Regular Article; Solitary waves; Theoretical; Traveling waves; Trigonometric functions; Variables
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2017-11571-0

. The double ( G / G , 1 / G )-expansion method is an influential, effective and well-suited method to examine closed form traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we extract abundant wave solutions to the (2+1)-dimensional typical breaking soliton equation and the (1+1)-dimensional classical Boussinesq equation through this method. The wave solutions are presented in terms of hyperbolic function, trigonometric function and rational function. By means of the wave transformation, the NLEEs are reduced to nonlinear ordinary differential equation (ODE) and then the nonlinear ODE is utilized to examine the necessary NLEE. The method can be considered as the generalization of the ( G / G -expansion method established by Wang et al. and it is shown that the suggested method is a powerful mathematical tool for investigating nonlinear evolution equations.