Breathers, multi-peak solitons, breather-to-soliton transitions and modulation instability of the variable-coefficient fourth-order nonlinear Schrödinger system for an inhomogeneous optical fiber

Abstract

Optical fiber communication system is one of the core supporting systems of the modern internet age. In this paper, under investigation is a variable-coefficient fourth-order nonlinear Schrödinger system, which describes the simultaneous propagation of the optical pulses in an inhomogeneous optical fiber. The first-order breathers are constructed. Breathers are converted into several types of the nonlinear waves, i.e., multi-peak solitons, antidark solitons, periodic waves and W-shaped solitons, under the transition condition. With the decrease of |λr+a2|, the peak number of a multi-peak soliton increases, where λr represents the real part of the spectral parameter and a is a real constant. Peak number reaches the maximum since the multi-peak soliton is transformed into a set of the periodic waves with λr+a2=0. Widths and velocities of the multi-peak solitons are related to the group velocity dispersion and fourth-order dispersion coefficients. We find that the condition of baseband modulational instability coincides with the transition condition when we use the rogue-wave eigenvalues, i.e., the transition between the rogue waves and multi-peak solitons can occur in the baseband modulational instability.