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By using the extended homogeneous balance method, the localized coherentstructures are studied. A nonlinear transformation was first established, and then thelinearization form was obtained based on the extended homogeneous balance method for thehigher order ( 2 + 1 ) -dimensional Broer-Kaup equations. Starting from this linearizationform equation, a variable separation solution with the entrance of some arbitrary functionsand some arbitrary parameters was constructed. The quite rich localized coherent structureswere revealed. This method, which can be generalized to other (2 + 1 )-dimensionalnonlinear evolution equation, is simple and powerful.