Abstract
Starting from a special Bäcklund transform and a variable separation approach, a quite general variable separation solution of the generalized (2+1)-dimensional perturbed nonlinear Schrödinger system is obtained. In addition to the single-valued localized coherent soliton excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
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