Localized coherent structures of the (2+1)-dimensional higher order Broer-Kaup equations

By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended homogeneous balance method for the higher order (2+1)_dimensional Broer_Kaup equations. Starting from this linearization form equation, a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed. The quite rich localized coherent structures were revealed. This method, which can be generalized to other (2+1)_dimensional nonlinear evolution equation, is simple and powerful.