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

Abstract

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.

Solitary wave solutions of the Vakhnenko–Parkes equation

“…which shows that the solitary waves will exist for b > 0 as long as n > 1/2 which is guaranteed from (5) and (10). The width of the solitary wave given by (12) or (13) is the same by virtue of (10).…”

“…In particular when n = 1, (14) collapses to Eqs. (3.4) of [11], (2) of [7], (3) of [8] and (2) of [10].…”

“…The theory of nonlinear evolution equations (NLEEs) is an important area of research in the area of applied mathematics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. A challenging task is to look for solutions of these NLEEs.…”

Travelling wave solutions for a surface wave equation in fluid mechanics

“…which de scribes os cil la tory Ray leigh-Marangoni in sta bil ity in a liq uid layer with free bound ary. The G'/G-ex pan sion method has be come widely used to search for var i ous ex act so lutions of NLEE re cently [5][6][7], the value of this method is that one treats non-lin ear prob lems by es sen tially lin ear meth ods. We first treat the gov ern ing eq.…”

Exact Solutions of Equation Generated by the Jaulent-Miodek Hierarchy by(G’/G)-Expansion Method

“…Moreover, Zhang et al have further extended the method to deal with evolution equations with variable coefficients [17]. In fact the ( / )-expansion method has been successfully applied to obtain exact solution for a variety of (NLEEs) [12,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In this paper, the ( / )expansion method is proposed for constructing more general exact solutions of the above nonlinear (2 + 1)-dimensional equation generated by the Jaulent-Miodek Hierarchy.…”