Application of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math>-expansion method to travelling wave solutions of three nonlinear evolution equation

Abazari, Reza

doi:10.1016/j.compfluid.2010.06.024

Cited by 53 publications

(35 citation statements)

References 37 publications

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“…In ( ) of our solutions, let = + and 0 = − 1 / 2 ; then it will be equivalent to Eq. (20) in [23]. Simply periodic solutions ( ) are new and cannot be degenerated through elliptic function solutions.…”

Section: Discussionmentioning

confidence: 99%

“…In recent years, many powerful methods for constructing the solutions of VPE have been used, for instance, the HirotaBacklund transformations method [19], the inverse scattering method [20,21], the exp-function method [22], and the ( / )-expansion method [23]. In this article, we would like to use the complex method [24][25][26] to obtain traveling wave solutions of VPE.…”

Section: Is Called the Vakhnenko-parkes Equation (Vpe)mentioning

confidence: 99%

See 1 more Smart Citation

Exact Solutions of the Vakhnenko-Parkes Equation with Complex Method

Yuan

Aminakbari

et al. 2017

Journal of Function Spaces

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Section: Discussionmentioning

confidence: 99%

Section: Is Called the Vakhnenko-parkes Equation (Vpe)mentioning

confidence: 99%

Exact Solutions of the Vakhnenko-Parkes Equation with Complex Method

Yuan

Aminakbari

et al. 2017

Journal of Function Spaces

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“…Validity: Abazari (2010) In addition, the obtained solutions ul 6 , ul 8 , u2 6 , u2 8 , u3 1 to u3 6 , u3 8 , u4 1 to u4 6 and u4 8 are new and have not presented in the earlier literature.…”

Section: Advantagesmentioning

confidence: 94%

New Approach of (<em>G\'/G</em>)-expansion Method for RLW Equation

Naher¹,

Abdullah²

2014

RJASET

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Abstract:In this study, new extension of the (G'/G)-expansion method with nonlinear ODE has been introduced to investigate the generalized regularized long wave equation. Therefore, many new travelling wave solutions with many parameters are generated. The obtained solutions are more general and solutions include the solutions, the hyperbolic function, the trigonometric function and the rational forms. In addition, some of our solutions are identical with already published results, which validate newly generated solutions and others solutions have not been reported in the previous literature.

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“…To illustrate both phenomena we focus on a paper that appeared recently in this journal [6]. In [6], the ( ′ / )-expansion method was applied to three nonlinear evolution equations that arise in the mathematical modelling of fluids.…”

mentioning

confidence: 99%

“…In [6], the ( ′ / )-expansion method was applied to three nonlinear evolution equations that arise in the mathematical modelling of fluids. For illustrative purposes we consider the solutions only for the first of these equations, namely the transformed reduced Ostrovsky equation (dubbed the Vakhnenko-Parkes equation in [6]…”

mentioning

confidence: 99%

Comment on “Application of -expansion method to travelling-wave solutions of three nonlinear evolution equation” [Comput Fluids 2010;39:1957–63]

Parkes

2011

Computers & Fluids

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The Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Comment on "Application of ( ′ )-expansion method to travelling wave solutions of three nonlinear evolution equation" [Computers & Fluids 2010;39:1957-1963 E.J. Parkes AbstractIn a recent paper [Abazari R. Application of ( ′ )-expansion method to travelling wave solutions of three nonlinear evolution equation. Computers & Fluids 2010;39:1957-1963, the ( ′ / )-expansion method was used to find travelling-wave solutions to three nonlinear evolution equations that arise in the mathematical modelling of fluids. The author claimed that the method delivers more general forms of solution than other methods. In this note we point out that not only is this claim false but that the delivered solutions are cumbersome and misleading. The extended tanh-function expansion method, for example, is not only entirely equivalent to the ( ′ / )-expansion method but is more efficient and user-friendly, and delivers solutions in a compact and elegant form.

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Application ofG′G-expansion method to travelling wave solutions of three nonlinear evolution equation

Cited by 53 publications

References 37 publications

Exact Solutions of the Vakhnenko-Parkes Equation with Complex Method

Exact Solutions of the Vakhnenko-Parkes Equation with Complex Method

New Approach of (<em>G\'/G</em>)-expansion Method for RLW Equation

Comment on “Application of -expansion method to travelling-wave solutions of three nonlinear evolution equation” [Comput Fluids 2010;39:1957–63]

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