Application of -expansion method to two nonlinear evolution equations

Comment on " Application of Improved - Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations, Adv. Appl. Math. Mech. 4(2012) 122-130"

“…Comparison between our results in this article and the well known results obtained in Ref. [19] will be given in Sec. 3.…”

“…3 of Ref. [19], the authors applied the improved ( / ) GG  -expansion method (1.4) and (1.5) and found the solutions(3.5)-(3.11) of [19] for the RLW equation (3.1) as well as the solutions (3.17)-(3.21) of [19] for the SLRW equation (3.12) which contain some minor errors due to the error in (1.6) and (1.7).…”

“…In Ref. [19] the authors proposed the improved ( / ) GG  -expansion method and found some solutions for each of two nonlinear evolution equations, namely the nonlinear RLW equation and the nonlinear SRLW equation.…”

Some new solutions of the (1+1)-dimensional PDE via the improved (G′/G)-expansion method

“…For example, Wazwaz [22], examined this equation to obtain exact solutions by using the sinecosine algorithm. Liu et al [23] In this article, we would like to apply the improved '/ G G -expansion method to reveal many new exact solutions of nonlinear equations, namely, the simplified MCH equation. One of the highlights is to deal with the nonlinearity of the simultaneous algebraic systems on the involved parameters and to show that there exist many new and more general traveling wave solutions.…”

Solving nonlinear evolution equation system using two different methods

“…Obtaining their explicit solutions is quite di cult. So far, with the development of soliton theory, many e cient methods for obtaining these exact solutions have been presented, such as Hirota bilinear tranformation [1], Darboux and Backlund transform [2], Weierstrass function method [3], symmetry method [4,5], Painleve analysis method [6], theta function method [7], Wronskian technique [8], homogeneous balance method [9,10], F-expansion method [11], sine-cosine method [12,13], exponential function method [14,15], inverse scattering method [16,17], functional variable method [18], extended tanh method [19], modi ed simple equation method [20,21], trial equation method [22], (G ′ /G)-expansion method [23,24], sub-equation method [25], auxiliary equation method [26] and so on. When we nd the exact solutions of nonlinear partial di erential equations by using the (G ′ /G)-expansion method, we obtain the solution in the terms of (G ′ /G).…”