Abstract
A modified CK direct method is generalized to find finite symmetry groups of nonlinear mathematical physics systems. For the (2 + 1)-dimensional Broer–Kaup–Kupershmidt (BKK) system, both the Lie point symmetry and the non-Lie symmetry groups are obtained by this method. While using the traditional Lie approach, one can only find the Lie symmetry groups. Furthermore, abundant localized structures of the BKK equation are also obtained from the non-Lie symmetry group.
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