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

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