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

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

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

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

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

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

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

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