Fractal Dromion, Fractal Lump, and Multiple Peakon Excitations in a New (2 + 1)-Dimensional Long Dispersive Wave System**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

By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.