General Solution and Fractal Localized Structures for the (2+1)-Dimensional Generalized Ablowitz-Kaup-Newell-Segur System

Using the standard truncated Painlevé expansions, we derive a quite general solution of the (2+1)-dimensional generalized Ablowitz-Kaup-Newell-Segur (AKNS) system. Except for the usual localized solutions, such as dromions, lumps, and ring soliton solutions, etc., some special localized excitations with fractal behaviour, i.e., the fractal dromion and fractal lump excitations, are obtained by some types of lower-dimensional fractal patterns.