Folded localized excitations of the (2+1)-dimensional (M+N)-component AKNS system

摘要

Starting from the standard truncated Painleve expansion and a multilinear variable separation approach, a quite general variable separation solution of the (2+1)- dimensional (M+N)- component AKNS (Ablowitz - Kaup - Newell - Segur) system is derived. In addition to the single-valued localized coherent soliton excitations like dromions, breathers, instantons, peakons, and a previously revealed chaotic localized solution, a new type of multi-valued ( folded) localized excitation is obtained by introducing some appropriate lower-dimensional multiple valued functions. The folded phenomenon is quite universal in the real natural world and possesses quite rich structures and abundant interaction properties.