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

The article studies the propagation of rogue waves with a nonautonomous NLSE in presence of external potential, which is considered as an important model for many physical phenomena in quantum mechanics. The obtained waves are of first and second-order, and are investigated using similarity transformation. The nonlinear dynamical behaviour of these waves has also been demonstrated in the presence of gravity and magnetic fields. The result shows the influence of gravity and magnetic fields over density, width and peak heights. Moreover, the modulation instability has also been discussed.