The functional separation method based on the singular manifold method

The functional separation method based on the singular manifold method may be devised to obtain a functional separation solution with arbitrary functions of a given nonlinear partial differential equation. Several examples are used to illustrate this approach, and their exact solutions are obtained. The localized coherent structures and their interaction properties are numerically studied on the basis of the exact solutions. The fission and fusion phenomena and the creation and annihilation phenomena of dromion-like structures are reported.