Abstract
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 homogenous 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 quire rich localized coherent structures were revealed. This method, which can be generalized to other (2+1)-dimensional nonlinear evolution equation, is simple and powerful.
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