Rogue Wave Solutions and Modulation Instability With Variable Coefficient and Harmonic Potential

Abstract

This article studies the propagation of rogue waves with a nonautonomous NLSE in the presence of external potential. This model is considered to be an important model for many physical phenomena in quantum mechanics and optical fiber. The obtained waves are of first and second order and are investigated using similarity transformation. The nonlinear dynamic behavior of these waves is also demonstrated with different parameter values for the magnetic and gravity fields. The results show the influence of these fields over density, width, and peak heights. Moreover, the modulation instability is also discussed.