Superposed Kuznetsov-Ma solitons in a two-dimensional graded-index grating waveguide

The 2 1-dimensional coupled nonlinear Schrödinger equation with distributed coefficients in a graded-index grating waveguide is investigated, and an exact two-breather solution for certain functional relations is obtained. From this solution, the superposed Kuznetsov-Ma (KM) solitons can be constructed. The explicit functions that describe the evolution of the peak, width, center, and phase are found exactly, from which one knows that diffraction and chirp factors play important roles in the evolutional characteristics, such as phase, center and widths, while the gain/loss parameter only affects the evolution of their peaks. Moreover, we can change the propagation type of the superposed KM solitons by adjusting the relation between the maximumeffective propagation distance Zm and the periodic locations Zij based on the maximum amplitude of the superposed KM solitons. The controllability for the type of excitation, such as partial excitation, maintenance, and postponement of the superposed KM solitons, is exhibited.