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A class of coherent structures and interaction behavior in Multidimensions

We solve the (2+1)-dimensional Davey-Stewartson (DS) equation, a multidimensional analog of the nonlinear Schrödinger equation. A rather general solution for the variables separation with two arbitrary functions is first obtained by applying a special Bäcklund transformation and introducing the seed solutions. And then some new special types of two-dimensional coherent structures are obtained. These structures exhibit interesting novel features not found in one-dimensional solitons.