Inverse design of extreme waves

Abstract

We examine the characteristics of the initial conditions leading to the appearance of freak waves of high amplitude within the framework of the nonlinear Schrödinger equation. We consider several of the most representative shapes of the waves with high amplitude as potential candidates for the rogue waves and obtain sufficient criteria for their parameters. We also estimate the maximum norm of the resulting rogue wave solution. The results pave the way for analysis of the properties of initial conditions that might lead to the occurrence of high amplitude field spikes in the applications governed by the nonlinear Schrödinger equation.