On modulation instability analysis and rogue waves in the presence of external potential: The (n + 1)-dimensional nonlinear Schrödinger equation

To study the rogue waves in (n + 1)-dimensions, we assume the (n + 1)-dimensional NLSE in the occurrence of external potential. The modulation instability (MI) analysis is also performed as it is considered the fundamental mechanism for the development of wave solutions because it signifies the exponential growth of a weak perturbation. As far as concerned about the rogue waves, the 1st and 2nd order solutions are obtained by similarity transformation which are localized in both spatial and temporal directions in the presence of external potential. Dynamical study shows the different wave behavior by selecting the appropriate values of parameters of external magnetic field.