Abstract
The new generalized (G'/G)-expansion method is one of the powerful and competent methods that appear in recent time for establishing exact solutions to nonlinear evolution equations (NLEEs). We apply the new generalized (G'/G)-expansion method to solve exact solutions of the new coupled Konno-Oono equation and construct exact solutions expressed in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. The significance of obtained solutions gives credence to the explanation and understanding of related physical phenomena. As a newly developed mathematical tool, this method efficiency for finding exact solutions has been demonstrated through showing its straightforward nature and establishing its ability to handle nonlinearities prototyped by the NLEEs whether in applied mathematics, physics, or engineering contexts.
Highlights
IntroductionMechanical, chemical, biological, engineering and some economic laws and relations appearMd
Various physical, mechanical, chemical, biological, engineering and some economic laws and relations appearMd
Our aim in this paper is to present an application of the new generalized (G′ G) -expansion method to the new coupled Konno-Oono equation to be solved by this method for the first time
Summary
Mechanical, chemical, biological, engineering and some economic laws and relations appearMd. Belgacem mathematically in the form of differential equations which are linear or nonlinear, homogeneous or inhomogeneous. Almost all differential equations relating physical phenomena are nonlinear. Methods of solutions of linear differential equations are reasonably easy and well avowed. The techniques of solutions of nonlinear differential equations are less obtainable and in general, approximations are generally used. The analytical solutions of such equations are of fundamental importance to reveal the inner structure of the phenomena. Nonlinear evolution equations (NEEs) are widely used as models to describe complex physical phenomena in various fields of sciences, especially in fluid mechanics, solid-state physics, plasma physics, plasma waves and biology, etc. Various methods have been utilized to explore different kinds of solutions of physical models described by nonlinear partial differential equations (NPDEs). In recent years, a variety of effective analytical and semi-analytical methods have been developed to be used for solving NLEEs, such as the inverse scattering transform method [1], the (G′ G ,1 G) -expansion method [2] [3], the modified simple equation method [4] [5], the Sumudu transform method [6]-[8], the homogeneous balance method [9] [10], the Darboux transformation method [11], the Backlund transformation method [12], the complex hyperbolic function method [13] [14], the (G′ G) -expansion method [15]-[25], the improved (G′ G) -expansion method [26], the collocation method [27] [28], the similarity reductions method [29] [30], the homotopy analysis method [31] [32], the spectral-homotopy analysis method [33]-[35], the Hermite-Pade approximation method [36] and so on
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