Superposed Akhmediev breather of the (3+1)-dimensional generalized nonlinear Schrodinger equation with external potentials

The one-to-one correspondence between a (3 + 1)-dimensional variable-coefficient nonlinear Schrodinger equation with linear and parabolic potentials and a standard nonlinear Schrodinger equation is given, and an exact superposed Akhmediev breather solution in certain parameter conditions is obtained. These precise expressions for the peak, width, center and phase indicate that diffraction and chirp factors influence the evolutional characteristics such as phase, center and width, while the gain/loss parameter only affects the evolution of the peak. Moreover, by modulating the relation between the terminal accumulated time T-e or the maximum accumulated time T-m and the accumulated time T-0 based on the maximum amplitude of Akhmediev breather, the controllability for the type of excitation such as postpone, maintenance and restraint of the superposed Akhmediev breather is discussed. (C) 2013 Elsevier Inc. All rights reserved.