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Symmetry and Exact Solutions of (2+1)-Dimensional Generalized Sasa–Satsuma Equation via a Modified Direct Method

In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groups of the well-known (2+1)-dimensional Generalized Sasa–Satsuma (GSS) equation. Second, based on a modified direct method proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained and the relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groups obtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equations are constructed by the relationship obtained in the paper between the new solution and known solution.