Abstract
In this paper an algebraic method is devised to construct uniformly a series of complete exact solutions for some nonlinear differential equations. For illustration, we apply the extended proposed method to revisit the nonlinear coupled physical system, the nonlinear variant Buossinesq equations (I), (II) and Hirota–Satsuma coupled KdV nonlinear equations. We construct successfully a series of new exact solutions including the soliton solutions and elliptic doubly periodic solutions with the aid of computerized symbolic computation.