Non-Lie symmetry groups and new exact solutions of a (2+1)-dimensional generalized Broer–Kaup system

By the modified CK’s direct method, the symmetry groups theorem of a (2+1)-dimensional generalized Broer–Kaup system is derived. Based upon the results, Lie point symmetry groups and new exact solutions of a (2+1)-dimensional generalized Broer–Kaup system are obtained.

Research highlights
► By the modified CK’s direct method, we obtain the theorems of general symmetry groups for the (2 + 1)-dimensional Generalized Broer–Kaup system (GBK system).
► Lie point symmetry groups of the GBK system can easily be obtained from the theorems.
► The theorems show us the relationship between new solutions and the old ones of GBK system.
► We derive many new solutions of GBK System from the known ones given by previous literatures.