Nonlinear Schrodinger Equation

Abstract

Rogue waves are fascinating destructive phenomena in nature that have not been fully explained so far [1-3]. Oceanographers commonly agree that linear theories cannot provide explanations for their existence[6,7]. Only nonlinear theories can explain the dramatic concentration of energy into a single "wall of water" well above the average height of the surrounding waves[3,8,9]. Among nonlinear theories the most fundamental is based on the nonlinear Schr odinger equation (NLSE)[6]. If the fundamental approach allows us to give a basic explanation, then it can be extended to more general ones which take into account the two-dimensional nature of the problem. Which is our main goal.