Painlevé analysis and symmetry group for the coupled Zakharov–Kuznetsov equation

The Painlevé property for the coupled Zakharov–Kuznetsov equation is verified with the WTC approach and new exact solutions of bell-type are constructed from standard truncated expansion. A symmetry transformation group theorem is also given out from a simple direct method. ► Painlevé property for coupled Zakharov–Kuznetsov system is verified by WTC method. ► Symmetry group for coupled ZK system is given out by a simple direct method. ► Bell-type solution for coupled ZK system is constructed from standard truncation.