RING SOLITONS, DROMIONS, BREATHERS AND INSTANTONS OF THE NLS EQUATION

Abstract

We Study the abundant localized coherent structures of the (2+1)-dimensional nonlinear Schr?dinger (NLS) equation which was derived from the fluid dynamics and plasma physics. Using a B?cklund transformation and the variable separation approach, we find there exist much more abundant localized structures for the (2+1)-dimensional NLS equation. The abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution. Some special types of the dromion solutions, breathers, instantons and ring type of solitons are discussed by selecting the arbitrary functions appropriately. The dromion solutions can be driven by some sets of straight-line and curved line ghost solitons. The dromion solutions may be located not only at the cross points of the lines, but also at the closed points of the curves. The breathers may breath both in amplitudes and in shapes.