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

Parkes, E.J. (2010) Observations on the basic (G′/G)-expansion method for finding solutions to nonlinear evolution equations. Applied Mathematics and Computation, 217. pp. 1759-1763. ISSN 0096-3003 (https://doi.org/10.1016/j.amc.2010.03.073)

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Abstract

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.

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