Superposed Akhmediev breather of the image-dimensional generalized nonlinear Schrödinger equation with external potentials Original Research Article

The one-to-one correspondence between a image-dimensional variable-coefficient nonlinear Schrödinger equation with linear and parabolic potentials and a standard nonlinear Schrödinger 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 image or the maximum accumulated time image and the accumulated time image 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.