General Solution and Localized Coherent Soliton Structures of the (2+1)-Dimensional Generalized Davey-Stewarson Equations**The project supported by the Foundation of “151 Talent Engineering” of Zhejiang Province and the Natural Science Foundation of Zhejiang Province of China under Grant No. 100039

Abstract

In this paper, the variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized Davey–Stewarson equations: . Applying a special Bäcklund transformation and introducing arbitrary functions of the seed solutions, an abundance of the localized structures of this model is derived. By selecting the arbitrary functions appropriately, some special types of localized excitations such as dromions, dromion lattice, breathers, and instantons are constructed.