A note on solitary travelling-wave solutions to the transformed reduced Ostrovsky equation

Parkes, E.J.

doi:10.1016/j.cnsns.2009.11.016

Cited by 26 publications

(13 citation statements)

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“…Unfortunately the author [1] does not suggest new results to the problem of integrability of systems (1) except trivial exercise on the application of the Hirota method to the Korteveg-de Vries equation. He has made the continuation of the errors that were discussed in papers [8][9][10][11][12][13][14][15].…”

Section: Commun Nonlinear Sci Numer Simulat J O U R N a L H O M E P Amentioning

confidence: 98%

A note on “A study on an integrable system of coupled KdV equations”

Muraved

2011

Communications in Nonlinear Science and Numerical Simulation

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Section: Commun Nonlinear Sci Numer Simulat J O U R N a L H O M E P Amentioning

confidence: 98%

A note on “A study on an integrable system of coupled KdV equations”

Muraved

2011

Communications in Nonlinear Science and Numerical Simulation

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“…One should always study a problem in eagle-eyed solving mode, and check the results with the computer interactively. Recently, Parkes [6][7][8] and Kudryashov [9][10][11][12][13] have been continuously alerting the authors for equivalent, disguised, and incorrect results. Unfortunately, a number of cases have appeared in the literature when solutions derived by the basic Exp-function method are irrelevant [14][15][16][17].…”

Section: Resultsmentioning

confidence: 99%

On the application of the Exp-function method to the KP equation for N-soliton solutions

Aslan¹

2012

Applied Mathematics and Computation

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a b s t r a c tWe observe that the form of the Kadomstev-Petviashvili equation studied by Yu (2011) [S. Yu, N-soliton solutions of the KP equation by Exp-function method, Appl. Math. Comput. (2011) doi:10.1016/j.amc.2010.095] is incorrect. We claim that the N-soliton solutions obtained by means of the basic Exp-function method and some of its known generalizations do not satisfy the equation considered. We emphasize that Yu's results (except only one) cannot be solutions of the correct form of the Kadomstev-Petviashvili equation. In addition, we provide some correct results using the same approach.Ó 2012 Elsevier Inc. All rights reserved.As is well known, the Kadomstev-Petviashvili equation ( where the coefficients a, b, and c can be chosen appropriately. In the literature, one can encounter some distinct forms of the KP equation such as KPI equation (the case a ¼ 6, b ¼ 1, c ¼ À3 of (1)) and KPII equation (the case a ¼ 6, b ¼ 1, c ¼ 3 of (1) (1) The author considers the KP equation asand claims that Eq. (2) admits the one-soliton solution (the formula (9) in [2]) uðx; y; tÞwhere b 1 , k 1 , and r 1 remain arbitrary. But, the formula (2) describes two equations which differ in the sign of their u yy -terms. The author does not mention which equation in (2) admits the function (3) as a solution. Moreover, the direct substitution of (3) into (2) results in the expression 0096-3003/$ -see front matter Ó

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“…The foregoing illustrative discussion exemplifies two deficiencies of the ( ′ / )-expansion method: firstly, that the method delivers solutions in a cumbersome form (see (11) with (12), or (13), for example) and secondly, that the solutions appear to contain more free parameters than is actually the case. Typically, each solution can be manipulated into a neater form which displays the correct number of free parameters.…”

mentioning

confidence: 99%

“…Twenty eight solutions were derived including 'many new' solutions. However, in [11] we showed that all twenty eight solutions may be reduced to 11 or 12 . In [13], the solutions 11 , 21 and 3 were derived via a method involving Laurent series.…”

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confidence: 99%

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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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A note on solitary travelling-wave solutions to the transformed reduced Ostrovsky equation

Abstract: Two recent papers are considered in which solitary travelling-wave solutions to the transformed reduced Ostrovsky equation are presented. It is shown that these solutions are disguised versions of previously known solutions.

Cited by 26 publications

References 11 publications

A note on “A study on an integrable system of coupled KdV equations”

A note on “A study on an integrable system of coupled KdV equations”

On the application of the Exp-function method to the KP equation for N-soliton solutions

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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