New interaction property of (2Â +Â 1)-dimensional localized excitations from Darboux transformation

Using the binary Darboux transformation for the (2 + 1)-dimensional dispersive long wave equation, the “universal” variable separable formula is extended in a different way. From the extended formula, much more abundant localized excitations with arbitrary boundary conditions for the dispersive long wave equation can be obtained. The results obtained via the multi-linear variable separation approach are only a special case of the first step binary Darboux transformation. Two special interacting solutions are explicitly given. Especially, one of the examples exhibits a new interacting phenomenon: a localized solitary wave (dromion) can force an extended wave (solitoff) go back.