Exact Excitation and Abundant Localized Coherent Soliton Structures of (2+1)-Dimensional Perturbed AKNS 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

A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special Bäcklund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite general solution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.