Abstract
A modified direct method is developed to find finite symmetrygroups of nonlinear mathematical physics systems. Applying themodified direct method to the well-known (2+1)-dimensionalasymmetric Nizhnik–Novikov–Vesselovequation and Nizhnik–Novikov–Vesselov equation,both the Lie point symmetry groupsand the non-Lie symmetry groups are obtained. The Lie symmetrygroups obtained via traditional Lie approaches are only specialcases. Furthermore, the expressions of the exact finitetransformations of the Lie groups are much simpler than thoseobtained via the standard approaches.
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