Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System

Abstract

Nonlinear Drinfeld-Sokolov system is studied analytically by using four different methods ((G′/G)-expansion, direct algebraic, different form of the (G′/G)-expansion methods, and direct integration) and the results are found numerically. New exact and numeric solutions are given and the comparison of the results obtained from these different methods, methods themselves and numerical results are discussed in detail. It is found that the (G′/G)-expansion and different form of the (G′/G)-expansion methods are really coincide and effective methods in the view of finding different solutions that cannot be obtained by using the direct integration for Drinfel-Sokolov system.

Exact solutions for two different non-linear partial differential equations

“…where e is an arbitrary integration constant [5]. Balancing the terms, V 3 and V ′′ , in Eq.18, we have following form of solution:…”

Exact Solutions of the Gardner Equation and their Applications to the Different Physical Plasmas

“…The original (G /G)-expansion method is generalized to find (G /G, 1/G)-expansion method [13]. Some applications of (G /G)-expansion method can be seen in [14][15][16][17][18]. As a pioneer work [19] has applied the two-variable (G /G, 1/G)-expansion method and found the exact solutions of Zakharov equations.…”

Analytic Solutions of the Schamel-KdV Equation by Using Different Methods: Application to a Dusty Space Plasma

“…[21] used different form of the (G ′ /G)-expansion method. Some application of this method to the different nonlinear differential equations can be found in [19,21]. The third type of the expansion method is called the (G ′ /G, 1/G)-expansion method which considers the generalization of the original (G ′ /G)-expansion method.…”

“…The first method is so-called the original (G ′ /G)-expansion method described by [18]. Some applications of this method can be seen in [18][19][20]. Ref.…”