General variable separation solution and new localized excitations for the (2 + 1)-dimensional nonlinear Schrödinger equation

By applying a special Bäcklund transformation, a general variable separation solution for the (2 + 1)-dimensional nonlinear Schrödinger equation is derived. In addition to some types of the usual localized excitations, such as dromions, lumps, ring solitons, oscillated dromions, and breathers, soliton structures can be easily constructed by selecting arbitrary functions appropriately. A new class of localized excitations, like fractal-dromions, fractal-lumps, peakons, compactons, and folded excitations of this system is found by selecting appropriate functions. Some interesting novel features of these structures are revealed.PACS Nos.: 05.45.–a, 02.30.Jr