In this article we conduct a broad numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, a widely used model of rogue wave generation and dynamics in deep water. NLS breathers rising over an unstable background state are frequently used to model rogue waves. However, the issue of whether these solutions are robust with respect to the kind o...

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breat...

Rogue waves are very mysterious and extra ordinary waves. They appear suddenly even in a calm sea hard to be predicted. Although nonlinear Schrödinger equation provides perspective, it alone can neither detect rogue nor provide complete solution problems. Therefore, some approximations still mandatory for both obtaining an exact predicting Such as Kundu–Mukherjee–Naskar (KMN) model which allows...