Painleve Analysis and Symmetries of the Hirota–Satsuma Equation

The singular manifold expansion of Weiss, Tabor and Carnevale [1] has been success-fully applied to integrable ordinary and partial differential equations. They yield infor-mation such as Lax pairs, Bäcklund transformations, symmetries, recursion operators, pole dynamics, and special solutions. On the other hand, several recent developments have made the application of group theory to the solution of the differential equations more powerful then ever. More recently, Gibbon et. al. [2] revealed interrelations be-tween the Painleve ̀ property and Hirota’s bilinear method. And W. Strampp [3] hase shown that symmetries and recursion operators for an integrable nonlinear partial dif-ferential equation can be obtained from the Painleve ̀ expansion. In this paper, it has been shown that the Hirota–Satsuma equation passes the Painleve ́ test given by Weiss et al. for nonlinear partial differential equations. Furthermore, the data obtained by the truncation technique is used to obtain the symmetries, recursion operators, some analytical solutions of the Hirota–Satsuma equation.