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1 Introduction
[1] Clarkson et al. (1997) presented a class of nonlinear third-order partial differential equations for studying symmetry reductions as follows: Equation 1 [Figure omitted. See Article Image.] where [varepsilon] , α , κ and ß are arbitrary constants. This equation was introduced by [2] Gilson and Pickering (1995). The special case of equation (1) is the Rosenau-Hyman equation for [varepsilon] =0, α =1, ß =3 and κ =0 which has appeared in [3] Rosenau and Hyman (1993) as follows: Equation 2 [Figure omitted. See Article Image.] The Rosenau-Hyman equation models the effect of nonlinear dispersion in the formation of patters in liquid drops ([3] Rosenau and Hyman, 1993). The numerical simulation of compactons, solitary waves with compact support applied to the Rosenau-Hyman K(p, p) equation by [4] Rus and Villatoro (2007b). In [5] Rus and Villatoro (2007a), three implicit finite difference methods based on Padé approximations in space are developed for the Rosenau-Hyman K(p, p) equation. Nonlinear evolution equations with cosine/sine compacton solutions including the Rosenau-Hyman equation and generalizations of Korteweg-de Vries equation are studied by [6] Rus and Villatoro (2009). Authors of [7] Rus and Villatoro (2008) developed numerical methods with second-order, fourth-order, sixth-order, and eighth-order approximations to the spatial derivatives obtained by means of the method of the modified equations applied to the Ismail-Taha finite difference scheme. [8] Bazeia et al. (2010) solved and obtained traveling wave solutions to the Rosenau-Hyman equation.
The semi-analytical methods (adomian decomposition method (ADM), homotopy perturbation method (HPM) and variational iteration method (VIM)) for solving nonlinear partial differential equations are known as the subject of extensive analytical and numerical studies. Therefore, approximate analytical solutions are searched and are introduced, among which we can mention ADM ([9], [10] Dehghan et al. , 2009, 2007; [11], [12], [13] Wazwaz, 1999, 2006, 2009; [14] Tatari and Dehghan, 2005; [15], [16] Adomian, 1984, 1994), VIM ([18], [17] Abdou and Soliman, 2005a, b; [19] Dehghan and Tatari 2008; [21], [20] Dehghan and Shakeri, 2008a, b; [23], [22] Tatari and Dehghan, 2007a, b; [24], [25] Shakeri and Dehghan, 2008a, 2007b) and HPM ([26], [27], [28] He, 2003, 2005, 2006a), homotopy analysis method ([29] Dehghan et al. , 2010b) and, etc.
For the solution of equation (2) by semi-analytical methods (ADM, HPM and...