21,533 research outputs found

    Comment on “Application of (G′/G)-expansion method to travelling-wave solutions of three nonlinear evolution equation" [Comput Fluids 2010;39;1957-63]

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    In a recent paper [Abazari R. Application of (G′ G )-expansion method to travelling wave solutions of three nonlinear evolution equation. Computers & Fluids 2010;39:1957–1963], the (G′/G)-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 (G′/G)-expansion method but is more efficient and user-friendly, and delivers solutions in a compact and elegant form

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

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    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

    A note on travelling-wave solutions to Lax's seventh-order KdV equation

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    Ganji and Abdollahzadeh [D.D. Ganji, M. Abdollahzadeh, Appl. Math. Comput.206 (2008) 438{444] derived three supposedly new travelling-wave solutions to Lax's seventh-order KdV equation. Each solution was obtained by a different method. It is shown that any two of the solutions may be obtained trivially from the remaining solution. Furthermore it is noted that one of the solutions has been known for many years

    Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations

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    The 'tanh-coth expansion method' for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic tanh-function expansion method which was developed in the 1990s. It usually delivers three types of solution, namely a tanh-function expansion, a coth-function expansion, and a tanh-coth expansion. It is known that, for every tanh-function expansion solution, there is a corresponding coth-function expansion solution. It is shown that there is a tanh-coth expansion solution that is merely a disguised version of the coth solution. In many papers, such tanh-coth solutions are erroneously claimed to be 'new'. However, other tanh-coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh-function method. Similar remarks apply to tan, cot and tan-cot expansion solutions

    Awe and Humility in the Face of Things: Somatic Practice in East-Asian Philosophies

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    Whereas the Platonic-Christian philosophical tradition in the West favours an ”ascent to theory’ and abstract reasoning, east-Asian philosophies tend to be rooted in somatic, or bodily, practice. In the philosophies of Confucius and Zhuangzi in China, and KÅ«kai and DÅgen in Japan, we can distinguish two different forms of somatic practice: developing physical skills, and what one might call ”realising relationships’. These practices improve our relations with others -- whether the ancestors or our contemporaries, the things with which we surround ourselves or the phenomena of nature -- by reducing egocentrism and increasing humility. Because they transform the practitioner’s experience, the major benefit of philosophies grounded in somatic practice is that they help close the gap between beliefs and behaviour, and between ideas and action

    A note on loop-soliton solutions of the short-pulse equation

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    It is shown that the N-loop soliton solution to the short-pulse equation may be decomposed exactly into N separate soliton elements by using a Moloney-Hodnett type decomposition. For the case N = 2, the decomposition is used to calculate the phase shift of each soliton caused by its interaction with the other one. Corrections are made to some previous results in the literatur

    Observations on the basic (G′/G)-expansion method for finding solutions to nonlinear evolution equations

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    The extended tanh-function expansion method for finding solutions to nonlinear evolution equations delivers solutions in a straightforward manner and in a neat and helpful form. On the other hand, the more recent but less efficient (G′/G)-expansion method delivers solutions in a rather cumbersome form. It is shown that these solutions are merely disguised forms of the solutions given by the earlier method so that the two methods are entirely equivalent. An unfortunate consequence of this observation is that, in many papers in which the (G′/G)-expansion method has been used, claims that 'new' solutions have been derived are often erroneous; the so-called 'new' solutions are merely disguised versions of previously known solutions

    A note on "new travelling wave solutions to the Ostrovsky equation"

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    In a recent paper by Yaşar [E. Yaşar, New travelling wave solutions to the Ostrovsky equation, Appl. Math. Comput. 216 (2010), 3191-3194], 'new' travelling-wave solutions to the transformed reduced Ostrovsky equation are presented. In this note it is shown that some of these solutions are disguised versions of known solutions

    On Completely Integrability Systems of Differential Equations

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    In this note we discuss the approach which was given by Wazwaz for the proof of the complete integrability to the system of nonlinear differential equations. We show that his method presented in [Wazwaz A.M. Completely integrable coupled KdV and coupled KP systems, Commun Nonlinear Sci Simulat 15 (2010) 2828-2835] is incorrect.Comment: 14 pages. This paper was sent to the Communications in Nonlinear Science and Numerical Simulatio

    Measurement of the W Mass at LEP2

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    The mass of the W boson has been measured by the LEP collaborations from the data recorded during the LEP2 programme at e+ e- centre of mass energies from 161 to 209 GeV, giving the result : mw = 80.450 +/- 0.039 GeV/c^2. This paper discusses the measurements of the W Mass from direct reconstruction of the invariant mass of the WW decay products, particular emphasis is placed on the evaluation of systematic errors. Results on the direct measurement of the W width are also presented.Comment: Contribution to XXXVIIth Moriond Electroweak Conference, March 2002. 6 pages, 3 figures This version with typos correcte
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