Modulation instability and modulated waves patterns of the generalized non-autonomous nonlinear Schrodinger equation

Abstract

In this work, we studied the behavior of the solitonic waves and localized waves in nonlinear optical fibers. We use the generalized non-autonomous NLSE with space- and time-dependent coefficients. To construct exact soliton solutions, we use the transformation hypothesis and the JEF method. For constant values of the space-and time-dependent coefficients, we have pointed out W-shaped bright soliton, dark soliton, and Jacobi elliptic function solutions. When we consider the dispersion relation as a periodic function, we obtain new characteristics of the solitonic waves. We have used numerical simulation to seek the modulation's unstable and stable modes. It results in modulated wave patterns emerging for strong enough values of the cubic and quintic nonlinearities, and for specific times of simulation, rogue waves and breather solitons emerge in the structure. We have also demonstrated that when the quintic nonlinearity is absent, the breathing behavior of the solitonic waves generates localized energy in the system.