Deep-water waves: On the nonlinear Schr{\"o}dinger equation and its solutions

TL;DR

This paper discusses the nonlinear Schr{"o}dinger equation's role in modeling deep-water wave propagation and explores its localized breather solutions that relate to rogue wave formation.

Contribution

It provides insights into the connection between breather solutions of the nonlinear Schr{"o}dinger equation and the emergence of rogue waves in deep-water environments.

Findings

Breather solutions can model rogue wave formation.

The nonlinear Schr{"o}dinger equation captures key dynamics of deep-water waves.

Potential implications for predicting extreme ocean waves.

Abstract

We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of extreme waves, also known as rogue waves or freak waves.