Eur. Phys. J. B 42, 581-589 (2004)
https://doi.org/10.1140/epjb/e2005-00018-6

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

Physics Science and Information Engineering School, Liaocheng University, Liaocheng 252059, P.R. China

Corresponding author: ^a lcced_bcl@lctu.edu.cn

Received: 7 April 2004
Revised: 8 October 2004
Published online: 18 January 2005

Abstract

Starting from the standard truncated Painlevé 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.