Abstract
The nonlocal symmetries for the ( 2 + 1 )-dimensional Kaup–Kupershmidt (KK) system are obtained with the truncated Painlevé method, and this kind of nonlocal symmetries can be localized to the Lie point symmetries by extending the original equation to a new system. Then the corresponding finite symmetry transformation group is computed. Furthermore, it is also proved that the ( 2 + 1 )-dimensional KK system is consistent Riccati expansion (CRE) solvable. By the CRE method, new interaction solutions between solitons and cnoidal waves are presented.
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