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Some New Lie Symmetry Groups of Differential-Difference Equations Obtained from a Simple Direct Method

In this paper, based on the symbolic computing system Maple, the direct method for Lie symmetry groups presented by Sen–Yue Lou [J. Phys. A: Math. Gen. 38 (2005) L129] is extended from the continuous differential equations to the differential-difference equations. With the extended method, we study the well-known differential-difference KP equation, KZ equation and (2+1)-dimensional ANNV system, and both the Lie point symmetry groups and the non-Lie symmetry groups are obtained.