General Solution and Fractal Localized Structures for the (2+1)-Dimensional Generalized Ablowitz-Kaup-Newell-Segur System
ZHENG Chun-Long1,2,3, ZHANG Jie-Fang3,4
1Department of Physics, Zhejiang Lishui Normal College, Lishui 323000
2Department of Physics, Zhejiang University, Hangzhou 310027
3Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004
4Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072
General Solution and Fractal Localized Structures for the (2+1)-Dimensional Generalized Ablowitz-Kaup-Newell-Segur System
ZHENG Chun-Long1,2,3;ZHANG Jie-Fang3,4
1Department of Physics, Zhejiang Lishui Normal College, Lishui 323000
2Department of Physics, Zhejiang University, Hangzhou 310027
3Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004
4Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072
Abstract：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.
2002, Vol. 19 
