Exact coherent structures in the (2 + 1)-dimensional KdV equations

Different from the (1 + 1)-dimensional nonlinear systems, (2 + 1) or higher dimensional nonlinear systems admit more rich coherent structures. Taking (2 + 1)-dimensional Korteweg de Vries (KdV for short) equations as an example, the singular manifold method is applied to search these coherent structures in an analytical form. With the aid of symbolic computation and plot representation of Maple, some coherent structures expressed in terms of new forms, such as dromions and solitoffs, have been illustrated by means of arbitrary functions in the analytical forms. In the paper, we will show these results by changing some specific choices for three different special cases for singular variable in details.